Thanks for watching everyone! As always, let me know what other topics to cover in future videos :) Also, you can check out my quantum mechanics playlist here for more videos: ua-cam.com/play/PLOlz9q28K2e4Yn2ZqbYI__dYqw5nQ9DST.html
Would you please upload details about"Pauli exclusion principal" like why this happened physics behind it.... Is Pauli exclusion principal the cause of repulsion........and details about it...
@@risavpokhrel7161 I've made a video on the Pauli Exclusion Principle before: ua-cam.com/video/INYZy6_HaQE/v-deo.html - let me know if this covers what you were looking for, or if you still have questions
So you're saying I should stop starting with representations of the Lorentz group to explain spin and angular momentum quantum numbers to my 5 year old nephew?
A grate video as per usual. I do have one request however: I as many others only learn about quantum mechanics through people like you and so it can be verry difficult to estimate how (over)simplified these explanations are. This can cause the Dunning Kruger Effect which you have probably already heard of (for those who haven’t: It is basically overconfidence as a result of not knowing how little one knows.). To avoid this it may be beneficial to point out some of the things you are leaving out and give little hints towards what else one can learn about these topics. This could also motivate some to learn more about each them. In any case, thank you for making these videos and have a wonderful day.
*THIS IS BY FAR ONE OF THE BEST EXPLANATIONS OF QUANTUM NUMBERS I'VE EVER HEARD😍😍😍😍* I still remember how frustrated I was when I was first introduced to Q. numbers @17. Now I'm 21 and this is a Eureka moment for me🥺🥺🤩😍🤩 thank you so much Parth 🙏🙏😭
Hey Parth and just wanted to say that How Grateful I am that you uploaded this Video as I currently have ATOMIC STRUCTURE in my Syllabus for High School and tho I know extra than my Colleagues(as I have some Depth of Quantum Mechanics' Basic, General and Special Relativity and other Physics Stuff), yet, this Topic seems a bit hard to me and your Video will mostly Help(As your way of teaching is Damn Great and I love the way you easily Explain some Hard Concepts!)
Whoa! That was lovely Parth. As a high school student, for me, this video was THE ONLY and the best explanation for quantum numbers which I didn't even understand earlier. Looking forward for more such content ❤️
Thank you Parth...This blew my mind. I am a pharmacist (essentially a kind of chemist) and this is the first time someone ever gives me a resonable explanation for these quantum numbers using orbital momentum to do so. Great video!
@@KalebPeters99 Search for properties of spherical harmonics. Or if you have scipy, look at them. >from scipy.special import sph_harm as Y >L = (some positive int) >M = list(range(-L, L+1)) pick theta and phi on the sphere and compute: >sum([abs(Y(m,L))**2 for m in M]) That sum will not depend on the angular coordinates. It because the set of Y's are 2L + 1 dimensional representation of SO(3)....which gets into the group theory stuff about orbitals. Wigner's Nobel prize. Parth should do a symmetries video. It is *DEEP*.
Hello sir I am a jee aspirants and I usually confused in quantum model of atom but from your this and some more videoes , I am feeling confident THANKS YOU SO MUCH SIR LOVE FROM INDIA ❤️❤️❤️❤️
GREAT Explanation! It would be nice if you explain in a similar way how this field of science, quantum mechanics, developed, evolved, what had been the thought process of the people who contributed to this field, why it didn't go another way around so on. Specifically, going through the thought process of developing theories about reality.
Hey Parth! love your videos especially your video in which u solve the Schrodinger eqn for a particle in an infinite square well, the normalization of the wave function video that followed, and the one on solving the Schrodinger eqn for the H-atom this video feels like an amazing continuation. I have watched all ur QM videos and on ur recommendation bought my first Quantum mechanics Textbook(The one by David Bohm). I was also wondering if you will be making videos on relativistic QM and explain the Klein-Gordon equation and The Dirac equation just the way u demystified the Schrodinger eqn!?? also, I just thought I'd mention it but I would absolutely love it if we could get more math videos like the ones on grad,div and curl u covered except maybe this time for something like Tensors so we can understand the Einstein field equation a wee bit better. thx for the amazing content man
There is nothing special about any particular choice of axes. The three p-orbitals along the axes form a basis in which a p-orbital with any orientation can be expressed by superposition. For example, an equal mixture of px and py states is equivalent to one oriented at 45 degrees between the x and y axes. They're like the components of a vector in 3D space, you can choose whatever coordinate system you want.
Thanks so much for these interesting videos! Can you help me understand why electrons have orbital angular momentum when we know electrons don't orbit around nucleus?
Does it mean if energy is not moving from one place to another place but is in one place for a long time (i.e within certain volume) then it can be called as mass/rest mass??Example:binding energy??
hi parth G for beautiful explanation when i teach in senior secodry school students i tell them them that total energy of electron can described in terms of position of electron, angular momentum of electron ,orbital angular momentum and spin angular momentum. am i right sir or not.
6:08 I thought there's only 4 different types of subshells? You're saying that the energy level dictates the number of subshells to fill but you still only have 3 (s,p and d) for the fourth energy level, and 4 for the fifth (s,p,d, and f) and no more after that (as far as I know). Does this mean that there's a whole other l value that's introduced in the fourth energy level or am I just confused about what you were trying to say there?
That's because energy levels for subshells aren't consistent with shell number. For example, if you look at transition metals, you can see that 4s subshells are filled before 3d subshells with some anomalies in elements like chromium, copper, etc. Likewise, it gets even more extreme with lanthanides and actinides. You fill out 5s, 5p and 6s before you start filling your first 4f subshell. The thing is, f subshells in 4th period atoms are completely empty. And likewise, periods 5+ have completely empty g, h, i subshells. Following periodicity of the elements, you'd probably only see the g subshell in period 8 and 9 elements, none of which are available, only theoretical.
More the electrons, more the number of orbitals and subshells....bcoz subshells usually gives the position of electrons and =1,2,3,4.... orbitals give the no. of energy levels (energy levels represents how much greater energy, that specific electron could have)
I think he just meant that max(l) = min(3, n-1). n still dictates what l is going to be, but that doesn't mean it's a strictly linear relationship for all n. Also, n=4 actually has 4 energy levels (s, p, d, and f).
@@pasijutaulietuviuesas9174 Wait is that actually true? I guess there's a lot of theorized future elements and I know about the whole mix up with row vs period number with the transition metals because of the potential energy, I just never thought about the possibility of orbitals past f. Are there diagrams for their possible subshell configurations (do you know)? I would be interested in seeing some of the wacky shapes that an orbital like that would make and I don't think we make those using empirical data. Or maybe we do! Come to think of it, how do we come up with the suborbital shell configurations?
I apologize for troubling you sir. I just wanted to ask a stupid question related to intrinsic angular momentum. Is intrinsic angular momentum (spin of electron) incorporated into the kinetic energy term of Schrodinger's equation or is it ignored? if so could you tell me why? I apologize if this question has offended or inconvenienced you in any way.
It is a good question. it is ignored in the schrodinger equation because a relativistic equation (the dirac equation) is required to incorporate spin. the problem is the dirac equation is so difficult and time intensive to solve, that it’s really not worth it if your goal is just to understand quantum numbers
Why does the spherical subshell has no angular momentum ,and isn't the angular momentum given by mvr,I have seen the mathematical derivation for angular momentum L=nhcross ,but isn't there an intuitive explanation for the angular momentum to include reduced planck's constant,if possible pls make a video on angular momentum of different subshells
your classical understanding of angular momentum will not hold in the quantum world. angular momentum ( and linear momentum) is not dependent on velocity in qm, mainly because these are features of waves. i recommend looking up the momentum of a wave rather than a particle
So is ang. momentum for electrons identical to classical AM but there are waves involved? I know spin is a misnomer since point objects aren't spinning like a pool ball. Or Football since you seem English or Aus. or something.
I know basically nothing about physics so sorry for the dumb questions. Are these quantities derived from the Hamiltonian and dictated by the Schrödinger equation? They kind of feel like emergent macroscopic quantities... Or are there some "quantum number operator" and a "quantum number basis", like there is for position and momentum? I've never been able to get a feel for what these mean.
quantum numbers arise from boundary conditions while solving the schrodinger equation. this is because the boundary conditions require periodic solutions for the wave function and there are infinitely many integer solutions for these boundary conditions. for the radial component we get the number n, for the orbital angular momentum we get l, and for spin angular momentum we get s. any combination of these 3 numbers will give you a (more or less) unique electron cloud configuration. you will get one quantum number per degree of freedom (basically the number of dimensions) of your system.
I have a doubt. Suppose you are trying to take away an electron from an atom. You will have to give more energy in order to take away the electron which is nearest to the nucleus than to the one which is farthest away. That is also the reason why valence electrons are mobile. Then how can shells closest to the nucleus have the least energy?? Please clear my doubt.
For an electron to escape an atom, it needs a certain amount of energy. The electrons closer to the nucleus having less energy is why they take more energy to extract, as you need to put in more energy to meet the escape threshold. A simpler example: imagine if there was a hole in the ground 2 meters deep, and there was a shelf/step a meter deep in the hole. A ball on the "floor" of the hole has a lower gravitational potential energy than a ball that's on the shelf. (Assuming each were 1kg, the potential energies would be -18.6 J for the lower ball, and -9.8 J for the ball on the shelf.) If you wanted to pull the balls out of the hole, it would take more energy to extract the lower ball (specifically, 18.6 J) than it would for the ball on the shelf (9.8 J). Just like the balls, an electron closer to the nucleus has a lower energy and therfore requires that we put in more energy to extract it.
@@nitsudrogers8087 see I have one more doubt then. See the electron closest to the nucleus will observe more force won't it?? Then shouldn't it have the most energy??
@@nandanair1373 a maximization of force is a minimization of potential energy. i suggest you carefully inspect the definition of potential energy, namely the negative sign
if an electron has no size is it a singularity? and whenever pi or e appears in an equation, it just cannot represent reality as pi and e have infintely many digits but a value like energy of electron cannot be infinitely precise. so h/(2pi) never be a value of anything real.
an electron has no definite exact size, not that it’s a singularity. this because electrons are really excitations in fields, with no same size each time. think water waves: each wave is not the same size as every other just because it’s all water. just because we cannot measure something with infinite precision doesn’t mean reality can’t have infinitely precise constants. it’s only pi and e themselves that have this problem, not the things they describe
wtf heisenberg's uncertainty principle dosen't state that you can perfectly know one of two features at a time, you never know a feature like position or momentum perfectly, because sigma would be zero in the relationship of momentum and position and that would be less than planck's constant.
There are conflicting thoughts on this. Remember, if you were to theoretically perfectly know one quantity (such as the position) then the uncertainty in momentum would be infinite. So the product between uncertainties would not be defined, and hence not necessarily less than Planck's constant. Some quantum physicists treat this in the following way: when we make a position measurement in an ideal / theoretical system, for a very, very small instant in time we know the exact position as the wave function collapses into the measured state, but the momentum uncertainty becomes infinite. Then the wave function evolves over time (following the Schrodigner Equation) from the instant after the measurement is made. But as I say, there are different thoughts on this depending on how "measurement" is dealt with.
Thanks for watching everyone! As always, let me know what other topics to cover in future videos :)
Also, you can check out my quantum mechanics playlist here for more videos: ua-cam.com/play/PLOlz9q28K2e4Yn2ZqbYI__dYqw5nQ9DST.html
Would you please upload details about"Pauli exclusion principal" like why this happened physics behind it.... Is Pauli exclusion principal the cause of repulsion........and details about it...
@@risavpokhrel7161 yes we need that...
@@risavpokhrel7161 yes i also have that question after watching the latest video on pbs space time
Thanks Parth, this was great!
Looking forward to the next part, hoping you get into explaining *spin* in some detail, I still don't quite get it hahah
@@risavpokhrel7161 I've made a video on the Pauli Exclusion Principle before: ua-cam.com/video/INYZy6_HaQE/v-deo.html - let me know if this covers what you were looking for, or if you still have questions
So you're saying I should stop starting with representations of the Lorentz group to explain spin and angular momentum quantum numbers to my 5 year old nephew?
Lol. How's the basement btw?
Haha on the contrary, I think that's the best place to start :D
big fan dude
A grate video as per usual. I do have one request however: I as many others only learn about quantum mechanics through people like you and so it can be verry difficult to estimate how (over)simplified these explanations are. This can cause the Dunning Kruger Effect which you have probably already heard of (for those who haven’t: It is basically overconfidence as a result of not knowing how little one knows.). To avoid this it may be beneficial to point out some of the things you are leaving out and give little hints towards what else one can learn about these topics. This could also motivate some to learn more about each them. In any case, thank you for making these videos and have a wonderful day.
that is a great idea
*THIS IS BY FAR ONE OF THE BEST EXPLANATIONS OF QUANTUM NUMBERS I'VE EVER HEARD😍😍😍😍*
I still remember how frustrated I was when I was first introduced to Q. numbers @17. Now I'm 21 and this is a Eureka moment for me🥺🥺🤩😍🤩 thank you so much Parth 🙏🙏😭
Hey Parth and just wanted to say that How Grateful I am that you uploaded this Video as I currently have ATOMIC STRUCTURE in my Syllabus for High School and tho I know extra than my Colleagues(as I have some Depth of Quantum Mechanics' Basic, General and Special Relativity and other Physics Stuff), yet, this Topic seems a bit hard to me and your Video will mostly Help(As your way of teaching is Damn Great and I love the way you easily Explain some Hard Concepts!)
Whoa!
That was lovely Parth. As a high school student, for me, this video was THE ONLY and the best explanation for quantum numbers which I didn't even understand earlier.
Looking forward for more such content ❤️
Thank you Parth...This blew my mind. I am a pharmacist (essentially a kind of chemist) and this is the first time someone ever gives me a resonable explanation for these quantum numbers using orbital momentum to do so. Great video!
Now we need a part 2 :)
4:53 note that all filled sub shells (fixed n, fixed l, all m_l, forget about spin for now) are perfectly spherical
Oh true? Is there somewhere with more info about this?
@@KalebPeters99 Search for properties of spherical harmonics. Or if you have scipy, look at them.
>from scipy.special import sph_harm as Y
>L = (some positive int)
>M = list(range(-L, L+1))
pick theta and phi on the sphere and compute:
>sum([abs(Y(m,L))**2 for m in M])
That sum will not depend on the angular coordinates. It because the set of Y's are 2L + 1 dimensional representation of SO(3)....which gets into the group theory stuff about orbitals. Wigner's Nobel prize.
Parth should do a symmetries video. It is *DEEP*.
Looking forward to video about other 2 quantum numbers
Hello sir I am a jee aspirants and I usually confused in quantum model of atom but from your this and some more videoes , I am feeling confident
THANKS YOU SO MUCH SIR
LOVE FROM INDIA ❤️❤️❤️❤️
Great Parth G Keep it Up, I love the way you teach and make us understand even the hardest topics.
Thank you PARTH, just learned something new about QM and uncertainty principle, we can know about more than one quantum states at the same time.
GREAT Explanation! It would be nice if you explain in a similar way how this field of science, quantum mechanics, developed, evolved, what had been the thought process of the people who contributed to this field, why it didn't go another way around so on. Specifically, going through the thought process of developing theories about reality.
For this you have to read a hole book, like Feyman lectures on Physics 3, it’s to much to explain in some Videos
thAT wAS aWESOME please make part two quickly.
Best of the Best explanations!
Hey Parth! love your videos especially your video in which u solve the Schrodinger eqn for a particle in an infinite square well, the normalization of the wave function video that followed, and the one on solving the Schrodinger eqn for the H-atom this video feels like an amazing continuation. I have watched all ur QM videos and on ur recommendation bought my first Quantum mechanics Textbook(The one by David Bohm). I was also wondering if you will be making videos on relativistic QM and explain the Klein-Gordon equation and The Dirac equation just the way u demystified the Schrodinger eqn!??
also, I just thought I'd mention it but I would absolutely love it if we could get more math videos like the ones on grad,div and curl u covered except maybe this time for something like Tensors so we can understand the Einstein field equation a wee bit better. thx for the amazing content man
Thank you for taking time to make such excellent videos, it’s very much appreciated
You are great bhaiya...no one can explain physics likes you
Amazing teacher ❤️❤️
Thanks very much!!!
Thankyouuuuuuuuuuuuuuuuu i had difficulty visualizing the theory 😭❤this video made everything clear within 10min!!
It scares me how I can understand your videos in one shot after attending my chemistry sirs lecture .God bless both of you ❤
I found the setup in this video to be the best compared to all others 😀
please bring the next video on ml and ms
Amazing video. You really deal with the most hardcore concepts in such a clear and reasonable simple way
Nice , greetings from Cairo
Well explained.
So good video, thanks
"how I fell in love with physics " video hairstyle you look like actor
For any of the asymmetric orbitals, what defines the X,Y & Z directions? Especially in the absence of a magnetic field (for example)
There is nothing special about any particular choice of axes. The three p-orbitals along the axes form a basis in which a p-orbital with any orientation can be expressed by superposition. For example, an equal mixture of px and py states is equivalent to one oriented at 45 degrees between the x and y axes. They're like the components of a vector in 3D space, you can choose whatever coordinate system you want.
Brilliant thanks
Could you make videos on double copy theory and twistor theory
Hey Parth, Please make vides on special theory of relativity. A request
You should look vaidic physics for understand quantum physics, cosmology, astrology, partical physics, plasma physics
Astrology is psuedo-science.
@@blindmoonbeaver1658 He didn't speak of Astrology .
@@jatinsharma5024 yes he did…
I was watching BBT when notification came 😂
Thanks so much for these interesting videos! Can you help me understand why electrons have orbital angular momentum when we know electrons don't orbit around nucleus?
good video ty
I'm hoping that this topic will lead to an explanation as to why the coinage metals (Cu, Ag, Au) tend to be univalent.
I need this for my foundation
🚽another floater
The alternative expression mentioned in the statement,1×(h/2π), does not apply here since it does not consider the factor of √l(l+1).
What about the magnetic ones?
How did we conclude that second subshell of n=2 is dumbell shaped ?
I wish I saw this guy before I failed Physics graduation.
Does it mean if energy is not moving from one place to another place but is in one place for a long time (i.e within certain volume) then it can be called as mass/rest mass??Example:binding energy??
Can give us same example
damn parth looks like the gym doing wonders for u
I think, in l=1 state angular momentum will be √2×(h/2π) not 1×(h/2π). Correct me , if I am wrong!
hi parth G for beautiful explanation when i teach in senior secodry school students i tell them them that total energy of electron can described in terms of position of electron, angular momentum of electron ,orbital angular momentum and spin angular momentum. am i right sir or not.
technically n, l, and m are all you need to describe the energy of an electron in a hydrogen atom
Boommm!!!!🔥
6:08 I thought there's only 4 different types of subshells?
You're saying that the energy level dictates the number of subshells to fill but you still only have 3 (s,p and d) for the fourth energy level, and 4 for the fifth (s,p,d, and f) and no more after that (as far as I know). Does this mean that there's a whole other l value that's introduced in the fourth energy level or am I just confused about what you were trying to say there?
That's because energy levels for subshells aren't consistent with shell number. For example, if you look at transition metals, you can see that 4s subshells are filled before 3d subshells with some anomalies in elements like chromium, copper, etc. Likewise, it gets even more extreme with lanthanides and actinides. You fill out 5s, 5p and 6s before you start filling your first 4f subshell. The thing is, f subshells in 4th period atoms are completely empty. And likewise, periods 5+ have completely empty g, h, i subshells. Following periodicity of the elements, you'd probably only see the g subshell in period 8 and 9 elements, none of which are available, only theoretical.
More the electrons, more the number of orbitals and subshells....bcoz subshells usually gives the position of electrons and =1,2,3,4.... orbitals give the no. of energy levels (energy levels represents how much greater energy, that specific electron could have)
I think he just meant that max(l) = min(3, n-1). n still dictates what l is going to be, but that doesn't mean it's a strictly linear relationship for all n. Also, n=4 actually has 4 energy levels (s, p, d, and f).
@@NateROCKS112 Oh right, I forgot that f started at 4 (in my head it was 5 for some reason).
@@pasijutaulietuviuesas9174 Wait is that actually true? I guess there's a lot of theorized future elements and I know about the whole mix up with row vs period number with the transition metals because of the potential energy, I just never thought about the possibility of orbitals past f. Are there diagrams for their possible subshell configurations (do you know)? I would be interested in seeing some of the wacky shapes that an orbital like that would make and I don't think we make those using empirical data. Or maybe we do! Come to think of it, how do we come up with the suborbital shell configurations?
Ok, I have baked stuff that looks like these orbitals using precisely quantized flour.
I apologize for troubling you sir. I just wanted to ask a stupid question related to intrinsic angular momentum. Is intrinsic angular momentum (spin of electron) incorporated into the kinetic energy term of Schrodinger's equation or is it ignored? if so could you tell me why? I apologize if this question has offended or inconvenienced you in any way.
It is a good question. it is ignored in the schrodinger equation because a relativistic equation (the dirac equation) is required to incorporate spin. the problem is the dirac equation is so difficult and time intensive to solve, that it’s really not worth it if your goal is just to understand quantum numbers
@@bobross5716 Thank you for the timely and informative reply! :)
some days later parth be like : circles are triangles
no offense
Love U bro
How and why s orbital has no angular momentum?
How does it rotates then in the spherical subshell without any angular momentum????
LOL you are asking a guy who repeats answers for an answer not in his book.
Big surprise you got a goose egg for an answer.
Why does the spherical subshell has no angular momentum ,and isn't the angular momentum given by mvr,I have seen the mathematical derivation for angular momentum L=nhcross ,but isn't there an intuitive explanation for the angular momentum to include reduced planck's constant,if possible pls make a video on angular momentum of different subshells
your classical understanding of angular momentum will not hold in the quantum world. angular momentum ( and linear momentum) is not dependent on velocity in qm, mainly because these are features of waves. i recommend looking up the momentum of a wave rather than a particle
Hi sir if an electron in s orbital l=0 but it must be possessing angular momentum as it ir revolving around nucleus then how l=0 ?
it is not…the whole point of the video is to show that the solar system model of the atom is wrong. it’s not a ball going around a nucleus
So is ang. momentum for electrons identical to classical AM but there are waves involved?
I know spin is a misnomer since point objects aren't spinning like a pool ball.
Or Football since you seem English or Aus. or something.
I know basically nothing about physics so sorry for the dumb questions. Are these quantities derived from the Hamiltonian and dictated by the Schrödinger equation? They kind of feel like emergent macroscopic quantities... Or are there some "quantum number operator" and a "quantum number basis", like there is for position and momentum? I've never been able to get a feel for what these mean.
quantum numbers arise from boundary conditions while solving the schrodinger equation. this is because the boundary conditions require periodic solutions for the wave function and there are infinitely many integer solutions for these boundary conditions. for the radial component we get the number n, for the orbital angular momentum we get l, and for spin angular momentum we get s. any combination of these 3 numbers will give you a (more or less) unique electron cloud configuration.
you will get one quantum number per degree of freedom (basically the number of dimensions) of your system.
I have a doubt. Suppose you are trying to take away an electron from an atom. You will have to give more energy in order to take away the electron which is nearest to the nucleus than to the one which is farthest away. That is also the reason why valence electrons are mobile. Then how can shells closest to the nucleus have the least energy?? Please clear my doubt.
For an electron to escape an atom, it needs a certain amount of energy. The electrons closer to the nucleus having less energy is why they take more energy to extract, as you need to put in more energy to meet the escape threshold. A simpler example: imagine if there was a hole in the ground 2 meters deep, and there was a shelf/step a meter deep in the hole. A ball on the "floor" of the hole has a lower gravitational potential energy than a ball that's on the shelf. (Assuming each were 1kg, the potential energies would be -18.6 J for the lower ball, and -9.8 J for the ball on the shelf.) If you wanted to pull the balls out of the hole, it would take more energy to extract the lower ball (specifically, 18.6 J) than it would for the ball on the shelf (9.8 J).
Just like the balls, an electron closer to the nucleus has a lower energy and therfore requires that we put in more energy to extract it.
@@nitsudrogers8087 yeah I understood. Thanks....
@@nitsudrogers8087 see I have one more doubt then. See the electron closest to the nucleus will observe more force won't it?? Then shouldn't it have the most energy??
@@nandanair1373 a maximization of force is a minimization of potential energy. i suggest you carefully inspect the definition of potential energy, namely the negative sign
You started working out, Parth?
Chemists (after learning QM effects): Life just got harder.
if an electron has no size is it a singularity? and whenever pi or e appears in an equation, it just cannot represent reality as pi and e have infintely many digits but a value like energy of electron cannot be infinitely precise. so h/(2pi) never be a value of anything real.
an electron has no definite exact size, not that it’s a singularity. this because electrons are really excitations in fields, with no same size each time. think water waves: each wave is not the same size as every other just because it’s all water.
just because we cannot measure something with infinite precision doesn’t mean reality can’t have infinitely precise constants. it’s only pi and e themselves that have this problem, not the things they describe
I am second
Hii bhai
SIR I JUST SENT YOU AN E-MAIL TO YOU.AS I NEED YOUR GUIDENCE.PLEASE HAVE A LOOK AT IT .
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wtf heisenberg's uncertainty principle dosen't state that you can perfectly know one of two features at a time, you never know a feature like position or momentum perfectly, because sigma would be zero in the relationship of momentum and position and that would be less than planck's constant.
There are conflicting thoughts on this. Remember, if you were to theoretically perfectly know one quantity (such as the position) then the uncertainty in momentum would be infinite. So the product between uncertainties would not be defined, and hence not necessarily less than Planck's constant.
Some quantum physicists treat this in the following way: when we make a position measurement in an ideal / theoretical system, for a very, very small instant in time we know the exact position as the wave function collapses into the measured state, but the momentum uncertainty becomes infinite. Then the wave function evolves over time (following the Schrodigner Equation) from the instant after the measurement is made. But as I say, there are different thoughts on this depending on how "measurement" is dealt with.
it would be useful to rephrase your question as it’s difficult to understand the heart of your question
All of this was replaced in 2002. See: “The Final Theory: Rethinking Our Scientific Legacy “,Mark McCutcheon. Try to keep up.
I wounder what the shell would look like if one, mathematically , forced all the quantum numbers to be the same ?