Fantastic he is back, some of the maths is too deep for me, but as he is doing it not me then it is still an enjoyable ride. At some point he will do the physics behind why money keeps disappearing from my wallet. My assumption is some sort of wave ( goodbye) function.
Okay, I wasn't ready to see how Pauli's exclusion principle can theoretically derive the bulk freaking modulus of solids! That is a level beyond insane!!!
Mahesh, Could you create a video explaining how the Higgs field changes the chirality of fermions between left-handed and right-handed states (using the chirality basis rather than the mass basis)? This mechanism explains how fermions acquire mass and proper time-it makes sense because the chirality changes enable fermions to have proper time, which corresponds to mass. Without this interaction, a left-handed fermion would remain left-handed indefinitely, similar to a photon, and thus, fermions would not have mass.
I'm retired and haven't thought about this stuff in years, yet find myself in the middle of the night watching it the whole way through. Younger up and coming scientists may not appreciate the gift of clear videos such as this, vs. trying to understand from a dry textbook, or dedicated time slot of a class. You can now learn when your mind is clearest and most receptive. The visual examples far exceed the chalkboard, and the ability to pause, rewind and replay cannot be understated. What a golden age of education, and how remarkable that Pauli could have formulated these concepts a century ago.
Couldn't agree more. I retired early partly to pursue studies I'd always wanted to do, and gained a masters degree in astrophysics. Even though it's somewhat more recent for me, these videos are not only a fantastic refresher but are giving me insights I never got while studying. I treat the _Physics Explained_ videos as a growing library of reference material and revisit them regularly. I'd highly recommend them as supplementary material to anyone studying physics or astrophysics.
despite of 1 year hiber, 3 videos in a row, from my very favorite physics channel? I must be dreaming. I don't use Patreon at all, because I myself is broken af but I think it's time to skip 3 meals per month just for this. I just can't have enough videos from him. best physics channel on youtube, because he touches very bottom of physics about "why this even?" rather than "how do we use this?".
Finally... I've been looking for this explanation for years. I calculated hundred of structure but never knew why steel doesn't come apart by itself when compressed. Feels like everything can just slip away. Thank you for the video.
You have returned in triumph! Absolutely love your stuff. Other channels give a heuristic, hand-wavy explanation of things, but you give us the real stuff. You are like the physics equivalent of 3blue1brown, and I wish more knew about this channel.
You’re on a roll with these. I started self studying physics with the help of your videos years ago. And now I’m graduating this spring with my condensed matter physics degree. Videos like yours were instrumental in helping feed my motivation and curiosity about the universe, please keep making them!
Hello! I'm currently on my first semester studying physics and I must say you've been a really big inspiration! I adore your videos and I thank you for everything you're doing. You're the best!
Your 3d quantum number lattice explains the structure of the periodic table, and made me think of a new? way of representing the table. The fact that energy follows a spherical growth also I think explains why there is some skipping of quantum numbers in larger atoms, because they are actually a lower energy.
Currently on my final year studying physics, my lecture classes in quantum mechanics, statistical physics, and every courses that involves semiconductors and even up to extend of astrophysics (quantum degeneracy pressure), I didn't like how my lecturer simply went through with stuffs like fermions having antisymmetric wavefunctions or just giving some random equation out of nowhere to explain things. Your approach of starting from scratch of infinite square well really give me the satisfaction of reminding me why I even decided to major in physics than other engineering fields in the first place. Well done
I am a student at UIUC studying nuclear engineering and chemistry, and I struggle to find good resources which fill in the small gaps between my classes. Nuclear and quantum are scarcely talked about in detail outside of academia. So to see such a well presented and thought out video covering the thin connection between chemistry (valance electron clouds) and quantum is like Prometheus taking a detour to bestow scarcely spoken knowledge. Thank you!
thermodynamics is a weird one, probably because the definitions aren't very clear, it was developed by engineers mostly and the language can be pretty vague, probably because a better formulation (statistical mechanics) already exists. It took me quite a bit of reading to understand the bulk of it, but I still don't have a clear view of the whole thing (especially around the gibbs free energy and potential functions part) my recommendation would be Thermal physics by Shroeder
thats true , i myself am an engineering student , and thermodynamics is the least intuitive subject for me , the definitions are pretty vague , but to be honest its not that hard to work around with , the exams are usually straight forward applications , but i cant digest it quite yet
@@ghrababderrahmen2457 yeah, reading Shroeder should give you a really good idea of Entropy and heat engines at least, that is a good place to start. All the vagueness about other things should go away after statistical mechanics, or so I have heard
I first discovered this channel studying "Turning Points" module at A-Level. This video takes me back to Chemistry as well, where we were told that "electrons don't like sharing energy levels >:(, they must flip first", truthfully, I'm grateful for because the math is far beyond me. Watching this video long after the fact has sparked a new way for me to think about chemical bonding. Thanks :)
6 днів тому+1
You might be interested in how ionic or covalent bonds are enabled by quantum mechanics. In particular, addition of angular momentum in QM, though it might be math heavy for some.
When the year is starting off with uncertainty to our rights and expression as humans, you bring mathematical clarity to some of the most foundational aspects of our lives. Thank you for this video
It is astonishing to explain an everyday world behaviour (you cannot pass through a wall) thanks to quantum mechanic. Thank you. Best scientific channel.
This is as entertaining as all the other "edutainment" channels out there. Unlike those channels, these videos actually go in-depth on the topic and you don't forget what you saw by tomorrow.
1000th like! Jokes aside, I like your content. Straight and to the point and based on the actual Maths involved. Great for students and scientists alike
Hey, I have a few questions that could make for an interesting future video if you're interested. It's about nuclear weapons and their blast mechanics. 1. When we see a nuclear blast in videos, there's an initial bright flash, followed by a sudden dimming, and then glowing, point-like shredded pieces scattering around before the brightness intensifies again. What's happening in this process? 2. In fission weapons, the blast intensity increases exponentially due to a chain reaction, where each fission event releases multiple neutrons that cause further reactions, rapidly escalating the energy release. But in fusion weapons, which are said to be more destructive than fission, how does the rate of energy release compare? Is it even more rapid? Would it follow a steeper exponential curve, or perhaps something like a factorial growth? 3. Antimatter weapons are purely theoretical at this point, but their potential blast mechanics are intriguing. How would an antimatter explosion compare to fusion or fission in terms of energy release patterns? If this isn't your area of expertise, that's totally fine, but I'd love to hear your thoughts or see a video on this in the future.
Thank you so much for these superb videos. You are pioneering a new science communication genre, aimed at an enormous audience: those of us with a bit of mathematical training and those untroubled by unfamiliar symbols, to see for the first time a much more real and actual model of nature. I am grateful. I hope you find making these videos rewarding and sustainable.
Yes mm well, getting the number of powers of 10 correct is of course well done. Thank you for the video, I'll probably revisit this one shortly. Pauli was quite a wizard with spectra and maths.
Great job, so few these days. Reminds me of Feynman's WHY on Horizon. A good visual is Understanding the Atom about electron spin etc. Love this channel.
You always considered non interacting particles in the derivations. But electrons repel each other. How big is the contribution of coulomb repulsion in the "hand thru the wall" idea?
Great video! To be nitpicky, in the case of the inability to push a hand through a wall, it’s more due to electrons resisting each other electrically, rather than the exclusion principle, right?
A wavefunction describing two particles should describe, for one thing, the probability of observing one in one location and the other in another location. As such, it should have two inputs for the two different locations. If you were just adding the two wavefunction, the resulting function would only have one input. Adding the two wavefunctions would, rather than corresponding to having two particles, would instead be a non-normalized wavefunction for a single particle, which would be a superposition of the two wavefunctions you started with (“superposition” just means “linear combination” after all).
Yeah, this guy's very good at explaining things and, importantly, he pitches it at the right level of mathematical detail. Enough for you to really see how the ideas "bite," but not so much that your eyes glaze over. It's excellent stuff. Good decisions about how deep to go, where to make approximations and where not to, etc.
13:02 The infinite square well basically requires that all probabilities at x coordinates 0 and 1 for either particle be zero. If we instead specify that the probabilities at x coordinates of 0 and 1 for a given particle be equal, we effectively end up with a circular space with no potential barrier anywhere. You can't have states of definite momentum in an infinite square well because the particles keep bouncing off the walls, but in our circular space, I believe our energy states for the particles end up each (except in the N=1 case) splitting into 2 momentum states, so the strict requirement of a spatially (anti)symmetric wavefunction goes away as long as no contour lines cut exactly perpendicular to the x1=x2 line, and as long as the x1=x2 line is a contour of the wavefunction of the energies of the particles are equal. Or something like that.
The problem with these kind of videos is this that there are so many non realistic assumptions in this and then they go on to derive such fragmented results of physics which is precisely the reason why physics has become too much fragmented today as we see it because of such fragmented approach.
Sir, we need about the all the six postulates postulates of quantum mechanics one by one in each video too that how they came with that idea. Respect and love from Nepal🙏🙏💞.
Okay I have a question: When we say distinguishable particles, what do we mean by that? Does that mean we need these particles are described by two seperate wavefunction rather than one?
It is worth noting that there is in fact one known natural process that can overcome the repulsion of Pauli Exclusion: the core of a supermassive star undergoing gravitational collapse. White Dwarfs are highly-compressed matter that is held up by electron degeneracy pressure, as electrons are forced into higher and higher energy states as they’re squeezed together. Neutron Stars are a similar thing, except with neutrons as the electrons and protons have been squeezed together. Once even that becomes not enough, the core collapses into a black hole.
AT 10:03, there was a question of "What is the solution?" But the previous question is "What is the problem?" You switched an exited number for a base state number and got a different probability density. It should be different and it appears different. What is the problem?
The problem is exactly that we got a different density. Not because we changed to base state but because we exchanged the particles. If the particles are indistinguishable then exchanging them must not change the physics. But a different probability density represents a different physical scenario.
@@narfwhals7843 Thank you for the response. But I assume that one particle which was in an excited state is now in the base state, and the one that was in the base state is now in the excited state and so they are no identical anymore. I suppose I am assuming that they "carry" the adjective "excited' (and whatever that implies in reality) down to the base state, while the other particle does the opposite. Thus, because they are in two different states, they are no longer indistinguishable. Perhaps the video is just not clear on what "swap the position labels" (at 8:56) means. And, is the density plotting done in reality or in modeling the formula alone?
In the 1D example of an infinite potential well, assuming there's a spin 'up' electron occupying the lowest energy state (E1), if we were to introduce another spin up electron into this system, would it change its spin to occupy E1 or would it occupy E2?
So all this assumes non-interacting particles, right? But electrons are negatively charged, they interact strongly with each other. Does that change the picture?
if the pauli exclusion principle causes matter to have structure then not falling through the floor is acceleration, where does this energy come from? It can resist gravity so there has to be energy use to balance that.
Best news of 2025 has been physicsexplained's sudden, unannounced, and unexpected return to making videos.
And Viascience too!
Let's then sit back and enjoy the ride...
Fantastic he is back, some of the maths is too deep for me, but as he is doing it not me then it is still an enjoyable ride.
At some point he will do the physics behind why money keeps disappearing from my wallet. My assumption is some sort of wave ( goodbye) function.
real!!
Real
Okay, I wasn't ready to see how Pauli's exclusion principle can theoretically derive the bulk freaking modulus of solids! That is a level beyond insane!!!
I came here by your post.. ❤️🔥
Just saw your community post and jumped here… thanks for the recommendation ❤
Came here from your recommendation ❤
Mahesh, Could you create a video explaining how the Higgs field changes the chirality of fermions between left-handed and right-handed states (using the chirality basis rather than the mass basis)? This mechanism explains how fermions acquire mass and proper time-it makes sense because the chirality changes enable fermions to have proper time, which corresponds to mass. Without this interaction, a left-handed fermion would remain left-handed indefinitely, similar to a photon, and thus, fermions would not have mass.
FR THAT'S INSANE
I'm retired and haven't thought about this stuff in years, yet find myself in the middle of the night watching it the whole way through. Younger up and coming scientists may not appreciate the gift of clear videos such as this, vs. trying to understand from a dry textbook, or dedicated time slot of a class. You can now learn when your mind is clearest and most receptive. The visual examples far exceed the chalkboard, and the ability to pause, rewind and replay cannot be understated.
What a golden age of education, and how remarkable that Pauli could have formulated these concepts a century ago.
Couldn't agree more. I retired early partly to pursue studies I'd always wanted to do, and gained a masters degree in astrophysics. Even though it's somewhat more recent for me, these videos are not only a fantastic refresher but are giving me insights I never got while studying. I treat the _Physics Explained_ videos as a growing library of reference material and revisit them regularly. I'd highly recommend them as supplementary material to anyone studying physics or astrophysics.
He’s not afraid to dig down deep into the math and explain it a bit
You're an amazingly talented educator.
despite of 1 year hiber, 3 videos in a row, from my very favorite physics channel? I must be dreaming.
I don't use Patreon at all, because I myself is broken af but I think it's time to skip 3 meals per month just for this. I just can't have enough videos from him.
best physics channel on youtube, because he touches very bottom of physics about "why this even?" rather than "how do we use this?".
Finally... I've been looking for this explanation for years. I calculated hundred of structure but never knew why steel doesn't come apart by itself when compressed. Feels like everything can just slip away.
Thank you for the video.
Bro is making banger after banger recently
You have returned in triumph! Absolutely love your stuff. Other channels give a heuristic, hand-wavy explanation of things, but you give us the real stuff. You are like the physics equivalent of 3blue1brown, and I wish more knew about this channel.
My man is dropping banger after banger, 2025 is off to a good start
Fantastic!
You’re on a roll with these. I started self studying physics with the help of your videos years ago. And now I’m graduating this spring with my condensed matter physics degree. Videos like yours were instrumental in helping feed my motivation and curiosity about the universe, please keep making them!
Float head physics
So glad you are back! 🎉
My first semester teaching (undergrad) QM by myself--so thankful you're back!!
Hello! I'm currently on my first semester studying physics and I must say you've been a really big inspiration! I adore your videos and I thank you for everything you're doing. You're the best!
Good choice my friend, have fun
His early video measuring the Earth to Sun is magnificent.
The elegance with which that video explains one of the fundamental principles of our cosmos, is astonishing.
I like how you don't skip intermediate steps in the calculations and don't jump to the final results.
News that I'm finally safe from falling through the floor can't come at a better time! Thank you for the patient, lucid explanation!
BRO LETS GOOOOOOOO.THIS GUY IS ONE OF THE BEST TEACHERS OUT THERE AND I AM
SO GRATEFUL HE IS BACK.LETS SUPPPORT HIM GUYS
Your 3d quantum number lattice explains the structure of the periodic table, and made me think of a new? way of representing the table. The fact that energy follows a spherical growth also I think explains why there is some skipping of quantum numbers in larger atoms, because they are actually a lower energy.
Currently on my final year studying physics, my lecture classes in quantum mechanics, statistical physics, and every courses that involves semiconductors and even up to extend of astrophysics (quantum degeneracy pressure), I didn't like how my lecturer simply went through with stuffs like fermions having antisymmetric wavefunctions or just giving some random equation out of nowhere to explain things. Your approach of starting from scratch of infinite square well really give me the satisfaction of reminding me why I even decided to major in physics than other engineering fields in the first place. Well done
I am a student at UIUC studying nuclear engineering and chemistry, and I struggle to find good resources which fill in the small gaps between my classes. Nuclear and quantum are scarcely talked about in detail outside of academia. So to see such a well presented and thought out video covering the thin connection between chemistry (valance electron clouds) and quantum is like Prometheus taking a detour to bestow scarcely spoken knowledge. Thank you!
Hey, that's cool! I also go to uiuc (EE though), and I only know like 1 npre major. What year are you?
bro please do a thermodynamics video , i am so screwed
I wish I had YT when I was taking thermodynamics 1 and 2 in the 1980s.
I am not screwed but I'd love to learn thermodynamics
thermodynamics is a weird one, probably because the definitions aren't very clear, it was developed by engineers mostly and the language can be pretty vague, probably because a better formulation (statistical mechanics) already exists. It took me quite a bit of reading to understand the bulk of it, but I still don't have a clear view of the whole thing (especially around the gibbs free energy and potential functions part)
my recommendation would be Thermal physics by Shroeder
thats true , i myself am an engineering student , and thermodynamics is the least intuitive subject for me , the definitions are pretty vague , but to be honest its not that hard to work around with , the exams are usually straight forward applications , but i cant digest it quite yet
@@ghrababderrahmen2457 yeah, reading Shroeder should give you a really good idea of Entropy and heat engines at least, that is a good place to start. All the vagueness about other things should go away after statistical mechanics, or so I have heard
I first discovered this channel studying "Turning Points" module at A-Level. This video takes me back to Chemistry as well, where we were told that "electrons don't like sharing energy levels >:(, they must flip first", truthfully, I'm grateful for because the math is far beyond me. Watching this video long after the fact has sparked a new way for me to think about chemical bonding. Thanks :)
You might be interested in how ionic or covalent bonds are enabled by quantum mechanics. In particular, addition of angular momentum in QM, though it might be math heavy for some.
Monsieur, you're spoiling us!! Chapeau. I remember doing this in the late 80s and marvelling. Also, the fun in 2 dimensions.
Cảm ơn bạn!
Amazing Job man! You condensed our 4 months of course within first 20 minutes. This is amazing!!
Yes yes yes, 3 gifts in January! Thank you so much. On this cold January night, I have something to keep me warm.
The wrap-up and conclution on this one was stellar, glad to have you back!
Is a spin statistic theorem video a possibility in future? Always happy to see this channel post new videos
best physics channel hands down
I have watched some of these at least 20 times, to the point where I can do the mathematics myself, and explain it well to others.
im gonna sleep so fucking good tonight and dream of quantum uncertainty, a beautiful combination
Spectacular! I always wondered about the fundamental basis of the Pauli exclusion principle. And you explained it so well.
Such a wonderful surprise this release!
It is like an escape into fantasy land. No politics, no woke ideology, just Bliss.
When the year is starting off with uncertainty to our rights and expression as humans, you bring mathematical clarity to some of the most foundational aspects of our lives. Thank you for this video
A clear and very gentle presentation of QM principles. Thank you very much.
It is astonishing to explain an everyday world behaviour (you cannot pass through a wall) thanks to quantum mechanic. Thank you. Best scientific channel.
Keep making physics content bro, your videos are so good, they are like my university lecture of physics
A tough subject covered in a remarkably concise manner. Kudos.
I didn't have the resolve to finish a physics degree, but I still like understanding what's going on. Your videos are just right for that
This is as entertaining as all the other "edutainment" channels out there. Unlike those channels, these videos actually go in-depth on the topic and you don't forget what you saw by tomorrow.
Many thanks for coming back! Great content and approach!
Thank you for this incredible, amazing, and extraordinary work.
I wish u could explain Kepler's law and how we can use them in real life.
Now this is my kinda video. Great stuff dude.
And once more he does it again, 40 min, it's like christmas again
Thank you very much for those amazing new videos. This is the best physics channel.
Your presentations are consistently excellent… and have a reassuring solidity.
Fantastic content, thanks for coming back
Man you are back!! Great please share more videos in depth..SRT. GRT etc...
Return of the King
1000th like! Jokes aside, I like your content. Straight and to the point and based on the actual Maths involved. Great for students and scientists alike
Glad you are uploading again. Thank you for all your help
It’s fascinating how we can reconstruct what we observe in reality from some simple mathematical assumptions. Extremely well explained!
These explanations and examples are on par with Griffiths and McIntyre readings. Please keep making videos !
We are truly spoilt here!
Thanks so much for your beautiful videos.
I’ve been awaiting your return and it has been well worth it!
Hey, I have a few questions that could make for an interesting future video if you're interested. It's about nuclear weapons and their blast mechanics.
1. When we see a nuclear blast in videos, there's an initial bright flash, followed by a sudden dimming, and then glowing, point-like shredded pieces scattering around before the brightness intensifies again. What's happening in this process?
2. In fission weapons, the blast intensity increases exponentially due to a chain reaction, where each fission event releases multiple neutrons that cause further reactions, rapidly escalating the energy release. But in fusion weapons, which are said to be more destructive than fission, how does the rate of energy release compare? Is it even more rapid? Would it follow a steeper exponential curve, or perhaps something like a factorial growth?
3. Antimatter weapons are purely theoretical at this point, but their potential blast mechanics are intriguing. How would an antimatter explosion compare to fusion or fission in terms of energy release patterns?
If this isn't your area of expertise, that's totally fine, but I'd love to hear your thoughts or see a video on this in the future.
Thank you so much for these superb videos. You are pioneering a new science communication genre, aimed at an enormous audience: those of us with a bit of mathematical training and those untroubled by unfamiliar symbols, to see for the first time a much more real and actual model of nature. I am grateful. I hope you find making these videos rewarding and sustainable.
I can't follow the maths well at all, but I could still see the logical progression you followed and I found it incredibly informative.
Yes mm well, getting the number of powers of 10 correct is of course well done.
Thank you for the video, I'll probably revisit this one shortly. Pauli was quite a wizard with spectra and maths.
Excellent video! Remarkable!
he’s back!
*scrolls a lil further*
with 3 videos oh my goddd
Great job, so few these days. Reminds me of Feynman's WHY on Horizon. A good visual is Understanding the Atom about electron spin etc. Love this channel.
Fantastic video. I just love your clarity
Return of the King 👑
You always considered non interacting particles in the derivations. But electrons repel each other. How big is the contribution of coulomb repulsion in the "hand thru the wall" idea?
OUTSTANDING video.
Great video! To be nitpicky, in the case of the inability to push a hand through a wall, it’s more due to electrons resisting each other electrically, rather than the exclusion principle, right?
Another excellent lecture.
3 videos in the space of 2 weeks. Do not stop cooking because I might kms getting through theoretical phys 2nd year without your videos 😂
amazing videos just as always, i am hoping to see next new videos soon
Are we allowed to use calculus on discrete value n?
Why is the wave function of 2 particles the product and not the sum of the wavefunctions?
Great question.
A wavefunction describing two particles should describe, for one thing, the probability of observing one in one location and the other in another location. As such, it should have two inputs for the two different locations. If you were just adding the two wavefunction, the resulting function would only have one input. Adding the two wavefunctions would, rather than corresponding to having two particles, would instead be a non-normalized wavefunction for a single particle, which would be a superposition of the two wavefunctions you started with (“superposition” just means “linear combination” after all).
he has retunred welcome back brother
Who came from Mhaesh's channel 😅❤
Not me, this came organically.
44:44 Ah, finally a Ghastly Expression. I've been deprived for so long!
Legitimately learned more in the first 3 minutes than in my quantum mechanics undergraduate course. 😐
Yeah, this guy's very good at explaining things and, importantly, he pitches it at the right level of mathematical detail. Enough for you to really see how the ideas "bite," but not so much that your eyes glaze over. It's excellent stuff. Good decisions about how deep to go, where to make approximations and where not to, etc.
Another great physicist entering the community.
13:02 The infinite square well basically requires that all probabilities at x coordinates 0 and 1 for either particle be zero. If we instead specify that the probabilities at x coordinates of 0 and 1 for a given particle be equal, we effectively end up with a circular space with no potential barrier anywhere.
You can't have states of definite momentum in an infinite square well because the particles keep bouncing off the walls, but in our circular space, I believe our energy states for the particles end up each (except in the N=1 case) splitting into 2 momentum states, so the strict requirement of a spatially (anti)symmetric wavefunction goes away as long as no contour lines cut exactly perpendicular to the x1=x2 line, and as long as the x1=x2 line is a contour of the wavefunction of the energies of the particles are equal.
Or something like that.
Fantastic video!
The problem with these kind of videos is this that there are so many non realistic assumptions in this and then they go on to derive such fragmented results of physics which is precisely the reason why physics has become too much fragmented today as we see it because of such fragmented approach.
Spin is mind bending.
This is reminding me of the quantum chemistry class I took a handful of years ago that I didn't really understand lol.
That's epic! Can you do thermodynamics too? I would love to learn it
Sir, we need about the all the six postulates postulates of quantum mechanics one by one in each video too that how they came with that idea. Respect and love from Nepal🙏🙏💞.
Masterpiece!
Another bager. Brilliant
Because of the collision check algorithm
Request you to make a detailed video on Einstein's general relativity
Great ❤❤❤
We love you man!
Okay I have a question: When we say distinguishable particles, what do we mean by that?
Does that mean we need these particles are described by two seperate wavefunction rather than one?
It is worth noting that there is in fact one known natural process that can overcome the repulsion of Pauli Exclusion: the core of a supermassive star undergoing gravitational collapse. White Dwarfs are highly-compressed matter that is held up by electron degeneracy pressure, as electrons are forced into higher and higher energy states as they’re squeezed together. Neutron Stars are a similar thing, except with neutrons as the electrons and protons have been squeezed together. Once even that becomes not enough, the core collapses into a black hole.
AT 10:03, there was a question of "What is the solution?" But the previous question is "What is the problem?" You switched an exited number for a base state number and got a different probability density. It should be different and it appears different. What is the problem?
The problem is exactly that we got a different density. Not because we changed to base state but because we exchanged the particles. If the particles are indistinguishable then exchanging them must not change the physics. But a different probability density represents a different physical scenario.
@@narfwhals7843 Thank you for the response. But I assume that one particle which was in an excited state is now in the base state, and the one that was in the base state is now in the excited state and so they are no identical anymore. I suppose I am assuming that they "carry" the adjective "excited' (and whatever that implies in reality) down to the base state, while the other particle does the opposite. Thus, because they are in two different states, they are no longer indistinguishable. Perhaps the video is just not clear on what "swap the position labels" (at 8:56) means. And, is the density plotting done in reality or in modeling the formula alone?
In the 1D example of an infinite potential well, assuming there's a spin 'up' electron occupying the lowest energy state (E1), if we were to introduce another spin up electron into this system, would it change its spin to occupy E1 or would it occupy E2?
So all this assumes non-interacting particles, right? But electrons are negatively charged, they interact strongly with each other. Does that change the picture?
appreciate your content! Let's gooooo!!!
Please make a video on general relativity
i waited so long
Please make videos about statestical mechanics
Amazing video! :D at 31:40 there's a little typo, where "State" is spelled "Spate"
if the pauli exclusion principle causes matter to have structure then not falling through the floor is acceleration, where does this energy come from? It can resist gravity so there has to be energy use to balance that.