@0:25 Review of quantum systems with finite number of pure states @7:15 Delta functions @16:05 Rules of probabilities in QM @34:50 Study of a particle on a circular line @39:55 Momentum operator @41:21 Eigenvector solution (pure state) of a momentum observable @45:20 Normalized form of momentum wave function @49:54 Allowable momentum values of a particle on a circular line @52:15 Origin of discreteness in QM @53:05 Angular momentum @59:00 QM vs classical mechanics @1:01:30 Compatible variables @1:06:38 Necessary and sufficient condition for compatibility --> zero commutator @1:08:35 Verifying that momentum and location operators do not commute (incompatible variables) @1:14:05 Commutator of location-momentum @1:19:10 Two-slit experiment: application of the wave function @1:26:36 Calculating probabilities for a super-positioned state from two slits on the vertical line @1:30:13 The puzzling phenomenon of interference @1:33:55 Momentum interpretation of the wave pattern on the vertical line @1:49:30 Explaining the wave function and probabilities for a single slit
Awesome storyteller! Leo Susskind is the master of the art to explain simply all relevant facts which make difficult matter easy to digest and understand.
Quantum Mechanics Lecture 3 Linear Operators = represent a cap leter with a triangle on top Example Ĥ ,Š,Â,Ŵ,Ŷ,Î,Ô,Ê and so forth ( note I used H cause k did not have a ^ on the top of it ) Ĥ|A> = |c> Let the operator act on A [Ĥ|A> ] H has acted on A Then add another vector B ( its correspondent ) ] = = Ĥba Way that you read it is that K acts on A to get a new vector Its called Matrix notation of Ĥ between vector A & B Remember the idea of a basis of vectors Labeled |n> pictured _/_ get a square table of Elements making a matrix Ð is the dimension of the space |A>= { An|n> n under a aswell {= the sum of 8:38 ( lecture3!) = Am That allows us to write any vector in the interesting form sum over m Example |A>= { |n> n this means { |n> = { |n> n = |A>= |A> Ĥ|A> = Now we take the inner product This is the nth component of the vector Ĥ acting on |A> or Ĥ times |A> Time to work this out = {< n|Ĥ|m> < m | A> Bracket over m ( sum over m) m From now on any thing under a braket will look like this {/m This below is the same at top = {/m < n|Ĥ|m> < m | A> Bracket over m ( sum over m) {/m < n|Ĥ|m> < m | A> = {/m Ĥnm Am You can multiply 2 linear Operators ĤŠ|A> = Ĥ[Š|A>] First act with Š on |A> after that hit the whole thing with Ĥ. ŠĤ is not neciarily the same as ĤŠ ĤŠ (Š|m> = {/r |r> ) Now writing everything written into component’s = {/r = (ĤŠ)nm = {/r Ĥnr Šrm ( long hand notation Hermitian Operators ( next ) ( Comes from Hermite ) Real This will stand with Lowercase ĥ They are matrix elements = < A| ĥ | B> * = isn’t real ? unless B=A So Hermitian Operators are interchangeable Linear Operators are not ĥ dose not have to be complex conjugated = *= Real Full definition of a Hermitian operator ĥab=ĥ*ba that’s ĥ being complex conjugated New concept eigon( german word ) value’s ( when the direction dosent change on the x axis 26:20 ( Lecture 3 ) Lets suppose we have a Hermitian operator with a igon vector landa (^) Ĥ|^>= ^|^> Will represent Eigon vectors and Eigon value’s with E 1 E-value’s of ĥ are real ( Real numbers ) That is Eigon values of Hermitian Operators are real 2 E-vectors of ĥ are orthonginal for ^1 not equal to ^2 3 ĥ have Ð mutraly orthonganal E-vectors . ( meaning same number of dominations) E-vectors multiply a E-vector by any number it still stays a E-vector 35:00( Lecture 3 ) Postulate of quantum mechanics . 1. states = collection of |A> ( ket vectors ) 2. things which you observe( measure ) ( observable’s ) =>ĥ 3. The value’s of observable ĥ are the Eigon values of ĥ 4. the state’s for which the observable ĥ is definite or certain as opposed to uncertain are the Eigon vectors of ĥ 5. arbitrary |A> ^,…… ^n |n> Now if you calculate the component of vector A( ket vector A ) < ^n|A> now ^n( which is a complex number ) and the d( direction ) Multiply it by its complex conjugate < ^n|A> = P(^n) or square it by its absolute value |< ^n|A>| squared This is the 5 postulate’s Jumping to the motion of a particle on a line 56:00 Describe this by X(t) ( classically) Quantumly were @ is Si @(X)=> |@(X)> Reminding rule 57:12 / Û is a X with a ^ . because X doesn’t have a ^ =@1x @2*(x) @(X) Û|@> = > @(X)= |X@X> Lets check if its Hermitian ( Breaking it apart ) Û|@(X)>= x@(x) Now the bra vector side @*(X) @*(X)X@(X) dx = Real number Now finding the E-vectors Û|@(X)>= ^|@> Find the function @ of X so you get a multiplied landa(^) Its impossible strickly speaking but you get close X@(X)=^@(X) Take all the equal to the left the (X-^)@(X)=0 Any place were X is not equal to ^ @ =0 @ is a function Were everything is zero except for x=^ -------------------------(x=^)-------------------------------- You can’t square it The derack delta function Is a function which is non zero over a tiny section . will allow that interval to shrink to zero The hight of the function |-| -----------------------------| |-------------------------------------- X=^ that’s a delta function D( tringal d with a squigally ) of X = 0 D(X - ^) 1:08:16 What a wave function really means (1:12:42) Lets take Si of X with Eigon value Landa(^)
B-hulll Shite! Leonard is a legend! His explanations aren't supposed to be a text book lecture. He takes you through the thought process and is always concise in what he says. Only people who really understand stuff can teach like this. Wish Leonard had taut me at Uni.. I love you man! Peace
Here's another good way to think of delta: take delta_eps to be the eps-wide, 1/-eps tall function, and think of taking the limit as eps goes to 0 of whatever integral you are calculating: limit as eps->0 from integral (delta_eps(x-y)*F(x) dx) = F(y)
youtube must think I'm a genius or something. Every morning lately this is playing. I must have "watched" this all the way through at least 10 times now
I'm taking QM now and his lectures hew closely to the ones being given at the undergraduate level. The reason I watch him is that he is a FAR better lecturer than the prof I have. Dr. Susskind has decades of classroom experience and my prof is teaching this for only the second time.
the information overlaps, causing the decoherence pattern. the two waves intersect, the information overlaps in certain bands creating the decoherence pattern and resulting in the infra red shift of the information.
@Kamran Nasir The Dirac delta replaces the Kronecker delta because the Dirac delta is zero at every value but x, just like the kronecker delta is zero everywhere but the non-zero components of each basis vector. Each Dirac delta is a basis vector in the space of all possible Dirac delta functions.
Could Heisenberg Uncertainty Principle be the same uncertainty that the observer will have with any future event? Could time and the geometry of spacetime be continuously formed by the momentum of EMR or light form one atom to another? There is no understanding of time in modern physics or why we have a future and a past. Could this be why we have the paradoxes of QM?
you seem to be missing the point: With QM you can show that the principles of CM - Newtons Laws of motion -hold for large bodies moving slowly. So, for instance, QM can be used to show how the moon moves round the earth. But the reverse is not true. CM cannot explain for example how an electron microscope works. QM contains CM QM >> CM
@mdinka ... listen to the definition of "compatible operators A and B"... having common eigenvectors (basis) of both operators simultaneously ONLY means that for a given state of a system, there will be a common basis (set of eigenvectors) that both A and B operators can act on at the moment of measurement and yield an observable eigenvalue a and b for each operator. There is no need to mention time as a dimension here!
@jamma246 He explains that the momentum changes along the y axis. At a given point, the momentum due to a slit is different of the momentum of the other ( that's why one is p and the other is q). The difference comes from the vertical momentum that a particle gains to get to a given point. If this point is in front of the slit, this vertical momentum is zero. If it's far away on the y axis, then it's a lot more. At least this was what i got from it :)
Possible explanation to the double slit experiment: 1. Charged particles have an associated magnetic field with them. 2. Protons and electrons are charged particles and have an associated magnetic field with them. 3. Photons also have both an electric component and a magnetic component to them. 4. Whenever a proton, electron, or photon is shot out of a gun, it's respective magnetic field interacts with the magnetic fields of the electrons in the atoms and molecules of the gun itself, the medium the projectile is going through (ie: air), and/or from around the slits themselves. 5. Via QED (quantum electrodynamics), newly generated photons might occur. 6. The projectile goes on it's own way and the newly generated photons go on their own way. It gives the illusion of a wave particle duality but is not that way in actual reality. 7. As far as detectors are concerned, they probably have an energy field that is one way when on and a different way when off. The interaction of this energy field, (or the lack thereof), with whatever is passing through it gives the indication that is observed.
xXxArnyxXx The theoretical idea would take into account the QED affects of the moving electron with it's associated moving magnetic field as it interacts with other magnetic fields from other electrons along the way. Newly generated photons might occur due to that interaction. The electron would go on it's own way and the newly generated photons would go on their own way.
@@schmetterling4477 a. Then explain how electron beam microscopes work. b. See also the 'Discussion' menu item on my page for my theory of everything idea, the potential completion of the periodic table of the elements, what space and time might actually be and more.
@@schmetterling4477 a. Okay, explain how with waves from quantum fields explains how electron beam microscopes work. b. It's possibly the literal TOE of the universe, it has everything to do with everything. (Dependent upon the results of the gravity test, which will speak for itself).
you don't just multiply psi by position or momentum operators and hope to get something useful.. you use psi in the schrodinger equation where it is multiplied by position and momentum to find the hamiltonian of the system. psi is a function dependent on time and position and the solution to the schrodinger equation makes the solution of psi an exponential function among other things
Joseph Von Fraunhofer 1787 to 1826 was a physicist and lens manufacturer known for the discovery of Fraunhofer offer lines( diffraction pattern from the sun), Fraunhofer diffraction, and Fraunhofer distance. Wikipedia, ain't it great!
It's amazing that when someone clearly competent in some field tries to teach something for enrichment of others, there come out of the wood-work those anonymous "experts" who fault them and claim they aren't doing it correctly, yet no evidence of the critic's expertise is anywhere to be found.
correction.. sorry i had not actually watched the video when i replied but your question of psi = e^p*x/h think of this as a solution to psi as before but not time dependent. also, there are good qm books you can buy online for less than $20 if you get the international versions(try griffiths).. if that is too expensive you can find them online i'm sure available for download for free. definitely a must to get a decent handle on everything (QM is hard!!)
I don't quite understand where the new equation for the wave function caused by the 2nd slit is coming from. Shouldn't it just be a displacement of the original function? I don't see why the momentum should be altered. Intuitively, I'd have thought that it would have just been the original function, but with y replaced by y+delta(x) where delta(x) is the displacement between the slits. So why has the momentum changed?
and then when he derives the double slit experiment, he uses phsi as exponential function after it passes through the slit , how well is he justified in assuming that ?
I did not understand the part in which he explained that how Kronecker delta is replaced by Diac delta function when me move from discreetness to continuity, in the first 30 minutes of the lecture, he made use of that when he was talking about the angular momentum of the particle with a large radius, where we tend to lose discreetness. Anyone please explain.
but if the electron gets a kick from the hole... isn´t it a measure as well? if the electron gets the kick, you could measure the impuls and say where the electron will hit the screen!?!? so, what has it to do with a wavefunction?
It’s very similar to water waves. With a single slit you have the waves so an oscillating function but the amplitudes on the wall (screen) will look like a blob. They vary on time but no oscillations on Y axis With a double slit or two sources you will get the pattern.
At 1;59.30-- you're seriously in error. The Frequency DOES NOT CHANGE. The phase of the wave incident on the detector plane changes; this is due to time of flight, as you imply, but it in no way represents a change in Frequency; which in fact is out of the question in this experimental arrangement. Get a Radio Engineer to explain it to you.
He's talking about the frequency of something else, I believe - the frequency of the wave function, not the frequency of whatever he's observing. I'd end with "get a physicist to explain it to you," but I don't want to sound like a jerk.
most do; but as he said a few times, a function on a complex variable can just be understood as the sum of two functions on a real variable, so you don't really need it
@theerterek ... that's really funny... btw Susskind is not a "pro teacher"... he's one of the most prolific theoretical physicists in the field of string theory among other related branches.
right... if e^p*x/h is a solution for psi then it is a solution to the schrodinger equation and describes the system and its energy states and so on, but remember in QM you cant have a definite known momentum. there is always a spread that follows from the standard deviation of the expectation values of p and x or E... and like i said you would need more info than just an exp function you would need to know if it was a solution, the argument here would describe a time dependence or energy etc.
@theerterek uhhh you ever think he does that maybe so he dont forget to bring up a point and keep things smooth and organized. dont speak unless you know what your talking about
well i am a starter in QM, i have 2 big doubts ! lemme first tell what i understood , there is phsi which defines a state of a system, phsi times x is a position operator and phsi 's derivative of x multiplied by i h is its momentum operator ... well then i operator these in phsi and what do i get in return, i mean what is the actual meaning of the result of operating phsi with position and momentum operator ?
The operator does not act on the state vector when mesuring it, the result of applying the operator to the state vector is just a part of the calculation of the "expectation" of the operator. The expectation of operator X is computed as , so X |Ψ> Is just the right part of the computation.
you should probably supplement your knowledge a little bit.. in QM we deal with p and x as operators and expectation values not definite values and classical variables. just remember that psi is just a function that must solve the schrodinger equation to mean anything psi itself isnt inherently something special, but if it is a solution you can use it for energy states and probability densities etc...
I'm taking QM now at the undergraduate level and his lectures are the same, except far better, then what I get now. QM as is being taught to me now requires linear algebra, but seems to be far more conceptual than math based right now.....at least at my level.
G_R_E_A_T__J_O_B with Dirac. Watching the rest of the videos today, who could dream that when R -> +oo, -> Ψ(p) where Ψ continuous (by using Dirac)!!!!!!
Thanks for the reply, well then what does this function tells us -> exp(p*x/h) ... ? i guess it gives us the phsi for a particle having a definite known momentum 'p'.. am i rite ?
psi times X is not the position operator, X itself is a position operator, it is a matrix, a hermitian matrix whose conjugate is equal to itself, when it is multiplied to psi(x), it is equivalent to psi(x) times a real number, now that real no. is the position of the particle, in state psi, but then for position, it has a value only at a particular point, and is zero everywhere else, (dirac del. func), I am a beginner too & that is what I have understood about X.
at 1.54 you state in an idealized experiment you would see no particles in the dark area of the interference ring. Wrong. Heisenberg's uncertainty principle; there are always particles in the dark area; always.
Heisenberg's uncertainty principle says the uncertainty in momentum times that in position is greater than some number. Why does that imply there ate particles where the probability solitude is 0?
Once again at 159.33 you pretend that vertical momentum has appeared by magic; this didn't happen. there is no frequency change; the circular wave fronts interfere because of PHASE changes due to time of flight; NO CHANGE OF MOMENTUM.
Science is not a religion and i dont care if Einstein says it; if some random guy on the internet says something better or correct i will go with the internet guy. I dont value science based on personal value (which in this materialistic world is mostly arbitrary) i value science on statements; facts and arguments. If a newborn can disprove general relativity i will go with the newborn baby.
At 0:13:00 An operation you do on a function! But his y parameter could be t instead, to make it clearer. The more symbols used the better : Leibniz to the MAX!
@@schmetterling4477 okay? what does that have to do with the OP? Obviously there is a distinction between lectures & field work. U got ur brownie points, now keep it moving
@@Tager253 It means that you can make all lectures free and you would be still nowhere. You can already get more than enough textbooks for free (in the library) and papers for free (library, internet) and you can read all of that day and night. Will that make you a scientists? No. Science is an apprenticeship. You have to live it. You have to breath it day and night. Sorry to disappoint you about that.
@@schmetterling4477 all that goes without saying, that's exactly why i said make them free so the coach can explain it. idk really what you're on but save it for the pastor my guy
Doesn't the collected electrons on the screen depends on the electric field force due to other electrons, and what happens in case of photons, as light are em waves, they are not charged particles, but they are the simultaneous effect of electric and magnteic fields from a distant source, bluvlu lbiblbibvlub blahaa,y brain stopped 😟😟
@0:25 Review of quantum systems with finite number of pure states
@7:15 Delta functions
@16:05 Rules of probabilities in QM
@34:50 Study of a particle on a circular line
@39:55 Momentum operator
@41:21 Eigenvector solution (pure state) of a momentum observable
@45:20 Normalized form of momentum wave function
@49:54 Allowable momentum values of a particle on a circular line
@52:15 Origin of discreteness in QM
@53:05 Angular momentum
@59:00 QM vs classical mechanics
@1:01:30 Compatible variables
@1:06:38 Necessary and sufficient condition for compatibility --> zero commutator
@1:08:35 Verifying that momentum and location operators do not commute (incompatible variables)
@1:14:05 Commutator of location-momentum
@1:19:10 Two-slit experiment: application of the wave function
@1:26:36 Calculating probabilities for a super-positioned state from two slits on the vertical line
@1:30:13 The puzzling phenomenon of interference
@1:33:55 Momentum interpretation of the wave pattern on the vertical line
@1:49:30 Explaining the wave function and probabilities for a single slit
Thx
❤thank you very much
The youtube algorithm, keeps feeding me all this knowledge for free, i absolutely love it
He is like a modern Socrates. I never hear him mention grades or tests, he is only interested in teaching this incredible knowledge
i would argue its the understanding that is useful but hey, to each their own. :)
Awesome storyteller! Leo Susskind is the master of the art to explain simply all relevant facts which make difficult matter easy to digest and understand.
Yes. 'You just replace the Dirac delta function with the Kronecker delta...' whew. Neurons overheating in that passage.
@@kertkaljusaar6763 huh?
Quantum Mechanics Lecture 3
Linear Operators = represent a cap leter with a triangle on top
Example Ĥ ,Š,Â,Ŵ,Ŷ,Î,Ô,Ê and so forth
( note I used H cause k did not have a ^ on the top of it )
Ĥ|A> = |c>
Let the operator act on A
[Ĥ|A> ] H has acted on A
Then add another vector B ( its correspondent )
] = = Ĥba
Way that you read it is that K acts on A to get a new vector
Its called Matrix notation of Ĥ between vector A & B
Remember the idea of a basis of vectors
Labeled |n> pictured _/_
get a square table of Elements making a matrix
Ð is the dimension of the space
|A>= { An|n> n under a aswell {= the sum of 8:38 ( lecture3!)
= Am
That allows us to write any vector in the interesting form sum over m
Example |A>= { |n>
n
this means { |n> = { |n>
n = |A>= |A>
Ĥ|A> = Now we take the inner product
This is the nth component of the vector Ĥ acting on |A> or Ĥ times |A>
Time to work this out
= {< n|Ĥ|m> < m | A> Bracket over m ( sum over m)
m
From now on any thing under a braket will look like this {/m
This below is the same at top
= {/m < n|Ĥ|m> < m | A> Bracket over m ( sum over m)
{/m < n|Ĥ|m> < m | A> = {/m Ĥnm Am
You can multiply 2 linear Operators
ĤŠ|A> = Ĥ[Š|A>]
First act with Š on |A> after that hit the whole thing with Ĥ.
ŠĤ is not neciarily the same as ĤŠ
ĤŠ (Š|m> = {/r |r> )
Now writing everything written into component’s
= {/r
= (ĤŠ)nm = {/r Ĥnr Šrm ( long hand notation
Hermitian Operators ( next ) ( Comes from Hermite )
Real
This will stand with Lowercase ĥ
They are matrix elements
= < A| ĥ | B> * = isn’t real ? unless B=A
So Hermitian Operators are interchangeable Linear Operators are not ĥ dose not have to be complex conjugated
= *= Real
Full definition of a Hermitian operator
ĥab=ĥ*ba that’s ĥ being complex conjugated
New concept eigon( german word ) value’s ( when the direction dosent change on the x axis
26:20 ( Lecture 3 )
Lets suppose we have a Hermitian operator with a igon vector landa (^)
Ĥ|^>= ^|^>
Will represent Eigon vectors and Eigon value’s with E
1 E-value’s of ĥ are real ( Real numbers )
That is Eigon values of Hermitian Operators are real
2 E-vectors of ĥ are orthonginal for ^1 not equal to ^2
3 ĥ have Ð mutraly orthonganal E-vectors . ( meaning same number of dominations)
E-vectors multiply a E-vector by any number it still stays a E-vector
35:00( Lecture 3 )
Postulate of quantum mechanics .
1. states = collection of |A> ( ket vectors )
2. things which you observe( measure ) ( observable’s ) =>ĥ
3. The value’s of observable ĥ are the Eigon values of ĥ
4. the state’s for which the observable ĥ is definite or certain as opposed to uncertain are the Eigon vectors of ĥ
5. arbitrary |A> ^,…… ^n |n>
Now if you calculate the component of vector A( ket vector A )
< ^n|A> now ^n( which is a complex number ) and the d( direction )
Multiply it by its complex conjugate
< ^n|A> = P(^n) or square it by its absolute value
|< ^n|A>| squared
This is the 5 postulate’s
Jumping to the motion of a particle on a line 56:00
Describe this by X(t) ( classically)
Quantumly were @ is Si @(X)=> |@(X)>
Reminding rule 57:12 / Û is a X with a ^ . because X doesn’t have a ^
=@1x @2*(x) @(X)
Û|@> = > @(X)= |X@X>
Lets check if its Hermitian
( Breaking it apart ) Û|@(X)>= x@(x)
Now the bra vector side @*(X)
@*(X)X@(X) dx = Real number
Now finding the E-vectors
Û|@(X)>= ^|@>
Find the function @ of X so you get a multiplied landa(^)
Its impossible strickly speaking but you get close
X@(X)=^@(X)
Take all the equal to the left the
(X-^)@(X)=0
Any place were X is not equal to ^ @ =0
@ is a function
Were everything is zero except for x=^
-------------------------(x=^)--------------------------------
You can’t square it
The derack delta function
Is a function which is non zero over a tiny section . will allow that interval to shrink to zero
The hight of the function
|-|
-----------------------------| |--------------------------------------
X=^ that’s a delta function D( tringal d with a squigally ) of X = 0 D(X - ^)
1:08:16
What a wave function really means (1:12:42)
Lets take Si of X with Eigon value Landa(^)
B-hulll Shite! Leonard is a legend! His explanations aren't supposed to be a text book lecture. He takes you through the thought process and is always concise in what he says. Only people who really understand stuff can teach like this. Wish Leonard had taut me at Uni.. I love you man! Peace
Here's another good way to think of delta: take delta_eps to be the eps-wide, 1/-eps tall function, and think of taking the limit as eps goes to 0 of whatever integral you are calculating:
limit as eps->0 from integral (delta_eps(x-y)*F(x) dx) = F(y)
youtube must think I'm a genius or something. Every morning lately this is playing. I must have "watched" this all the way through at least 10 times now
Algorithm keeps progressing more for me as well. These videos help me pass out because they bore me
@@prestonwilliams5244 llllmlllllllllll
P
P
Great job with δ(x)! Really great job!
I'm taking QM now and his lectures hew closely to the ones being given at the undergraduate level. The reason I watch him is that he is a FAR better lecturer than the prof I have. Dr. Susskind has decades of classroom experience and my prof is teaching this for only the second time.
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the information overlaps, causing the decoherence pattern. the two waves intersect, the information overlaps in certain bands creating the decoherence pattern and resulting in the infra red shift of the information.
@Kamran Nasir The Dirac delta replaces the Kronecker delta because the Dirac delta is zero at every value but x, just like the kronecker delta is zero everywhere but the non-zero components of each basis vector. Each Dirac delta is a basis vector in the space of all possible Dirac delta functions.
Amazing lecture
Could Heisenberg Uncertainty Principle be the same uncertainty that the observer will have with any future event? Could time and the geometry of spacetime be continuously formed by the momentum of EMR or light form one atom to another? There is no understanding of time in modern physics or why we have a future and a past. Could this be why we have the paradoxes of QM?
you seem to be missing the point:
With QM you can show that the principles of CM - Newtons Laws of motion -hold for large bodies moving slowly. So, for instance, QM can be used to show how the moon moves round the earth.
But the reverse is not true. CM cannot explain for example how an electron microscope works.
QM contains CM
QM >> CM
@mdinka ... listen to the definition of "compatible operators A and B"... having common eigenvectors (basis) of both operators simultaneously ONLY means that for a given state of a system, there will be a common basis (set of eigenvectors) that both A and B operators can act on at the moment of measurement and yield an observable eigenvalue a and b for each operator. There is no need to mention time as a dimension here!
But you can also express x and p in terms of ladder operators and when they act on psi they adjust the energy state
@jamma246 He explains that the momentum changes along the y axis. At a given point, the momentum due to a slit is different of the momentum of the other ( that's why one is p and the other is q).
The difference comes from the vertical momentum that a particle gains to get to a given point. If this point is in front of the slit, this vertical momentum is zero. If it's far away on the y axis, then it's a lot more.
At least this was what i got from it :)
Possible explanation to the double slit experiment:
1. Charged particles have an associated magnetic field with them.
2. Protons and electrons are charged particles and have an associated magnetic field with them.
3. Photons also have both an electric component and a magnetic component to them.
4. Whenever a proton, electron, or photon is shot out of a gun, it's respective magnetic field interacts with the magnetic fields of the electrons in the atoms and molecules of the gun itself, the medium the projectile is going through (ie: air), and/or from around the slits themselves.
5. Via QED (quantum electrodynamics), newly generated photons might occur.
6. The projectile goes on it's own way and the newly generated photons go on their own way. It gives the illusion of a wave particle duality but is not that way in actual reality.
7. As far as detectors are concerned, they probably have an energy field that is one way when on and a different way when off. The interaction of this energy field, (or the lack thereof), with whatever is passing through it gives the indication that is observed.
xXxArnyxXx
The theoretical idea would take into account the QED affects of the moving electron with it's associated moving magnetic field as it interacts with other magnetic fields from other electrons along the way. Newly generated photons might occur due to that interaction. The electron would go on it's own way and the newly generated photons would go on their own way.
@@charlesbrightman4237 Electrons are quanta. They aren't "going" anywhere. The entire idea that quanta have paths is false.
@@schmetterling4477 a. Then explain how electron beam microscopes work.
b. See also the 'Discussion' menu item on my page for my theory of everything idea, the potential completion of the periodic table of the elements, what space and time might actually be and more.
@@charlesbrightman4237 a) with waves from quantum fields. b) none of that has anything to do with electrons.
@@schmetterling4477 a. Okay, explain how with waves from quantum fields explains how electron beam microscopes work.
b. It's possibly the literal TOE of the universe, it has everything to do with everything. (Dependent upon the results of the gravity test, which will speak for itself).
That man defies the laws of physics, literally.
1:58:30 Oh thank god. We don't want to waste electrons needlessly when we can recycle our electrons.
Excellent teacher
i fell asleep on youtube and woke up at 1:43:33 paused
Hahah same Broo 😂 I don't how i landed here on this channel....i completed his 4-5 videos🥲
❤thank you very much publisher
Understood and getting interested in quantum mechanics
you don't just multiply psi by position or momentum operators and hope to get something useful.. you use psi in the schrodinger equation where it is multiplied by position and momentum to find the hamiltonian of the system. psi is a function dependent on time and position and the solution to the schrodinger equation makes the solution of psi an exponential function among other things
Joseph Von Fraunhofer 1787 to 1826 was a physicist and lens manufacturer known for the discovery of Fraunhofer offer lines( diffraction pattern from the sun), Fraunhofer diffraction, and Fraunhofer distance. Wikipedia, ain't it great!
Very rude and without class...
I'm Canadian (like that matters) and I find him (Susskind) thoughtful, kind, and a master of his work.
great lecture and great questions session at the end. thank you!
It's amazing that when someone clearly competent in some field tries to teach something for enrichment of others, there come out of the wood-work those anonymous "experts" who fault them and claim they aren't doing it correctly, yet no evidence of the critic's expertise is anywhere to be found.
where? these comments are all thank yous as far as i can see.
correction.. sorry i had not actually watched the video when i replied but your question of psi = e^p*x/h think of this as a solution to psi as before but not time dependent. also, there are good qm books you can buy online for less than $20 if you get the international versions(try griffiths).. if that is too expensive you can find them online i'm sure available for download for free. definitely a must to get a decent handle on everything (QM is hard!!)
I don't quite understand where the new equation for the wave function caused by the 2nd slit is coming from. Shouldn't it just be a displacement of the original function? I don't see why the momentum should be altered. Intuitively, I'd have thought that it would have just been the original function, but with y replaced by y+delta(x) where delta(x) is the displacement between the slits. So why has the momentum changed?
and then when he derives the double slit experiment, he uses phsi as exponential function after it passes through the slit , how well is he justified in assuming that ?
I did not understand the part in which he explained that how Kronecker delta is replaced by Diac delta function when me move from discreetness to continuity, in the first 30 minutes of the lecture, he made use of that when he was talking about the angular momentum of the particle with a large radius, where we tend to lose discreetness. Anyone please explain.
but if the electron gets a kick from the hole... isn´t it a measure as well? if the electron gets the kick, you could measure the impuls and say where the electron will hit the screen!?!? so, what has it to do with a wavefunction?
It’s very similar to water waves. With a single slit you have the waves so an oscillating function but the amplitudes on the wall (screen) will look like a blob. They vary on time but no oscillations on Y axis With a double slit or two sources you will get the pattern.
how many points might a particle be associated with?
At 1;59.30-- you're seriously in error. The Frequency DOES NOT CHANGE. The phase of the wave incident on the detector plane changes; this is due to time of flight, as you imply, but it in no way represents a change in Frequency; which in fact is out of the question in this experimental arrangement. Get a Radio Engineer to explain it to you.
The observable frequency of the wave is not the same as the probability wave frequency, S talks about the latter!
He's talking about the frequency of something else, I believe - the frequency of the wave function, not the frequency of whatever he's observing. I'd end with "get a physicist to explain it to you," but I don't want to sound like a jerk.
I too am Canadian and agree completely.
Are there any programing languadges that have a complex number data type
most do; but as he said a few times, a function on a complex variable can just be understood as the sum of two functions on a real variable, so you don't really need it
If we concentrate it is easy to understand
@theerterek ... that's really funny... btw Susskind is not a "pro teacher"... he's one of the most prolific theoretical physicists in the field of string theory among other related branches.
but is it a senior undergraduate level quantum mechanics class?
Thank you very very very very + very^1000 much for these great lectures ...
right... if e^p*x/h is a solution for psi then it is a solution to the schrodinger equation and describes the system and its energy states and so on, but remember in QM you cant have a definite known momentum. there is always a spread that follows from the standard deviation of the expectation values of p and x or E... and like i said you would need more info than just an exp function you would need to know if it was a solution, the argument here would describe a time dependence or energy etc.
@theerterek uhhh you ever think he does that maybe so he dont forget to bring up a point and keep things smooth and organized. dont speak unless you know what your talking about
If you "measure" the impulse, the wavefunction collapses.
How many state vectors are there?
well i am a starter in QM, i have 2 big doubts ! lemme first tell what i understood ,
there is phsi which defines a state of a system, phsi times x is a position operator and phsi 's derivative of x multiplied by i h is its momentum operator ...
well then i operator these in phsi and what do i get in return, i mean what is the actual meaning of the result of operating phsi with position and momentum operator ?
The operator does not act on the state vector when mesuring it, the result of applying the operator to the state vector is just a part of the calculation of the "expectation" of the operator. The expectation of operator X is computed as , so X |Ψ> Is just the right part of the computation.
It's 8 years now hopefully you have learned most of Quantum physics , isn't it ?
So , what do you do for a living 😃 just curious
you should probably supplement your knowledge a little bit.. in QM we deal with p and x as operators and expectation values not definite values and classical variables. just remember that psi is just a function that must solve the schrodinger equation to mean anything psi itself isnt inherently something special, but if it is a solution you can use it for energy states and probability densities etc...
Is this senior undergraduate level quantum mechanics?
The natural question is, does U= F + O in area 51 ?
I'm taking QM now at the undergraduate level and his lectures are the same, except far better, then what I get now. QM as is being taught to me now requires linear algebra, but seems to be far more conceptual than math based right now.....at least at my level.
G_R_E_A_T__J_O_B with Dirac. Watching the rest of the videos today, who could dream that when R -> +oo, -> Ψ(p) where Ψ continuous (by using Dirac)!!!!!!
Thanks for the reply, well then what does this function tells us -> exp(p*x/h) ... ? i guess it gives us the phsi for a particle having a definite known momentum 'p'.. am i rite ?
Yes you're right.
wow, he looks exactly like doc from back to the future
i listen to this while i do hw in hopes of absorbing that knowledge! lol
psi times X is not the position operator, X itself is a position operator, it is a matrix, a hermitian matrix whose conjugate is equal to itself, when it is multiplied to psi(x), it is equivalent to psi(x) times a real number, now that real no. is the position of the particle, in state psi, but then for position, it has a value only at a particular point, and is zero everywhere else, (dirac del. func), I am a beginner too & that is what I have understood about X.
dang 1/5th of the class is gone and were only of the 4th lecture
33:02
Knew about maths and postulates of quantum mechanics
Knew more about quantum mechanics
You are not quite correct..What about Richard Feynman and Walter Lewin?Exclusion Principle should be modified :P
@RavellaMusic "move at very good pieces" - what the fuck could that possibly mean? I guess I must have meant speeds.
at 1.54 you state in an idealized experiment you would see no particles in the dark area of the interference ring. Wrong. Heisenberg's uncertainty principle; there are always particles in the dark area; always.
Heisenberg's uncertainty principle says the uncertainty in momentum times that in position is greater than some number. Why does that imply there ate particles where the probability solitude is 0?
Once again at 159.33 you pretend that vertical momentum has appeared by magic; this didn't happen. there is no frequency change; the circular wave fronts interfere because of PHASE changes due to time of flight; NO CHANGE OF MOMENTUM.
You do know who this guy is, right? If Susskind says something, and some random dude on the internet says something else, I'm going with Susskind.
Science is not a religion and i dont care if Einstein says it; if some random guy on the internet says something better or correct i will go with the internet guy. I dont value science based on personal value (which in this materialistic world is mostly arbitrary) i value science on statements; facts and arguments. If a newborn can disprove general relativity i will go with the newborn baby.
He says this to make you enthusiastic about quantum mechanics. You have the feeling you discovered something.
lol i am currently taking this class and every lecture i try to keep awake.
Luis Luque's exclusion principle : "A single human being cannot simultaneously be a great physicist and a awesome teacher"
1:40:05
At 0:13:00 An operation you do on a function! But his y parameter could be t instead, to make it clearer.
The more symbols used the better : Leibniz to the MAX!
Feynman
same here bro. Im in 10th and havnt taken physics yet but am in advanced math and I have no idea what hes talking about lol
Go back to 1:41
let me go back playing cod, this blows my mind
But...
0+0(0)=?
Magician!!!
make education free Stan all lectures
Education is a lot more than just lectures.
@@schmetterling4477 okay? what does that have to do with the OP? Obviously there is a distinction between lectures & field work. U got ur brownie points, now keep it moving
@@Tager253 It means that you can make all lectures free and you would be still nowhere. You can already get more than enough textbooks for free (in the library) and papers for free (library, internet) and you can read all of that day and night. Will that make you a scientists? No. Science is an apprenticeship. You have to live it. You have to breath it day and night. Sorry to disappoint you about that.
@@schmetterling4477 all that goes without saying, that's exactly why i said make them free so the coach can explain it. idk really what you're on but save it for the pastor my guy
@@schmetterling4477 nobody wanna become no scientist that's for the gifted gifted, idk what ur projecting, so it must be U
Correct
Leonardo is the king Of Physics...But,no body cares..he deserves a statue..
thankyou
I was watching carlito how did o get here-
I have never seen, so far that Leonard has defined bra/kat, he just introduced them, and thought that everyone understod them.
He defines them in a previous video.
Great question session. Thank you Sir.
Doesn't the collected electrons on the screen depends on the electric field force due to other electrons, and what happens in case of photons, as light are em waves, they are not charged particles, but they are the simultaneous effect of electric and magnteic fields from a distant source, bluvlu lbiblbibvlub blahaa,y brain stopped 😟😟
Same doubt
very realistic
that's a weird thing to declare... and how is it a fact?
sure?
#rolfsmeets
my QM teacher sucks!!He says just do the math, forget the concepts!!!
If you want to see my work on something called Law of Pertainment theoratical physics
ｄっだ
I wouldn't waste logical replies to idiots. It makes them feel like they have a purpose in life, and nobody needs illusions ; )
I give up
Classical Mechanics > Quantum Mechanics. FACT.
lol every video has less and less viewers than the last one
Luis Luque I am astounded that this comment doesn't have more thumbs up!!!!
Haha!
U mad?
That lame guy is a pioneer on string theory, he surely wouldn't know much about quantum mechanics.
the class was boring!
This guy isn't a very compelling lecturer. He seems nervous, at least in the few minutes I watched
Grace and peace to you from God our Father and the Lord Jesus Christ - TRUST JESUS - LIVE FOR JESUS CHRIST and you will have everlasting life !