Thank you so much for the great explanation ! I live in Algeria and I'm a first year college student in industrial sciences. At the chemistry course they just tell us to skip the pure mathemetical part of quantum chemistry and simply apply it to quantum numbers and orbitals. I always wanted to truly get the math behind it, and your channel is exactly what I needed. Thank you again sir !
Thanks for sharing, Salim. Good luck as you continue in your studies. Your curiosity and willingness to dig deep to understand things beyond the expectations of your course work will prove very valuable as you progress in your career and life.
My material science prof decided not to go over this at all because "surely you've all already familiar with the Schrödinger equation", which we chemistry students, in fact, were not. So this was such a great and clear explanation of this model! Thank you!
Your explanation was fabulous. I've been struggling a bit with quantum chem at my uni and it made everything clear about the particle in a box. Thank you! Salutations from Brazil.
@@PunmasterSTP It went great! I passed with an 8.5, if I recall correctly. I'm now doing my PhD in organic synthesis, and this knowledge is still extremely useful for me. Thanks again :)
@@rodrigogomes5950That's awesome you passed, and even more awesome that you're using your knowledge with what you're doing now! I hope your research continues to go well.
I got stuck on a video about the maxwell boltzmann distribution in a channel called tonya coffey (great channel by the way) because of this very concept of energy in different nodes of waves so i searched online in google and youtube i found this video which i will definitely share this with my quantum enthusiastic friends. Amazing video TMP from India
PIB? More like "Perfect videos for me!" Thanks for sharing. On another note, the first time I saw this material I thought it was so cool that we could derive a "quantum number", after having seen them being described (but not derived) in gen chem.
@ 2:35 Remember that 2.m.E = 2.m.(1/2.m.v^2) = m^2 . v^2 = p^2 . So k = p / h-bar ! @ 6:54 There is only 1 quantum-number here because this is a 1-dimensional situation.
Is there any more elegant way of finding the form of psi than by just guessing that it should be of the form Asinkx+Bcoskx and differentiating twice to find what k should be? I was looking for some way of finding that sin and cos form rather than just knowing it.
In contrast to the normal wave equation whose solution is a linear combination of the eigenfunctions, here, because of quantization of energy, must the solution be only ONE of the eigenfunctions?
@S R Thank you & My apologies, i must have been out of my mind. My comments were intended for the video "Quantum Chemistry 3.9 - Average Position" ruclips.net/video/sCeUFzxowuQ/видео.html
@@TMPChem Thank you & My apologies, i must have been out of my mind. My comments were intended for the video "Quantum Chemistry 3.9 - Average Position" ruclips.net/video/sCeUFzxowuQ/видео.html
Note: The very nature of reality is probably analog (interacting energy modalities). Now sure, digitizing an analog universe would allow an entity to accurately do stuff, but it still would not be how actual reality would actually be. Science has to get off of their 'particle mentality' to try to discern the actual Theory Of Everything. Currently, science is coming up with things like 'virtual particles' because they are stuck on a particle mentality. A virtual particle does not exist in actual reality, it's 'virtual'. Edit: and likewise, an imaginary number 'i', is an imaginary number.
Hi Jo. We are guessing a trial function for Psi(x) which is Acos(kx) + Bsin(kx). When we take the second derivative of this function, it can be factored into the form [ -k^2 (Acos(kx) + Bsin(kx)) ]. So we have a negative constant squared times Psi(x) is equal to the second derivative, just as our light blue equation requires. In order for these equations to be equal, -k^2 must be equal to -2mE / hbar^2, which we can solve for the value of k given in orange.
I really don't get the assumption of why V(x)=0... You are saying there is a box (with infinite height???) and as long as the particle remains between x and l (i.e. inside the box, since its impossible escape from the top which is infinitely high) it's potential energy is 0? I mean, first off how do you know anything at all about the potential energy(s) of the particle? What does the fact that its stuck in a box have to do with potential energy and what kind of potential energy are you talking about? The way you are saying it is like it has ZERO potential energy in the box no matter its interaction with the surrounding, its position or the forces acting on it.
Hi Adam. For the purposes of analysis of the system, it doesn't matter what the energy is inside the box, it just matters that whatever the energy is inside the box, it's the same everywhere, and the boundary is infinitely high so that the particle is incapable of escaping. Having a flat potential energy surface (PES) inside the box means that the derivative of the potential everywhere inside the box is zero, which means there is no force acting on the particle except for the walls, where an infinitely strong force keeps the particle inside the box. We could just as easily define the energy inside the box to be 1, 2, or any other finite real number and the wavefunctions would be exactly the same, with the energy offset by the value we chose V(x) to be. Since this value is arbitrary, it is most convenient to choose that arbitrary value to be zero, which is why we've done that. As for why we know this, it's a model system and those are the parameters we've defined. They are true by definition. The usefulness of the model is how closely it corresponds to real systems to provide insight into their behavior.
sir if v(x) = infintity.....means......could u pls give me little intimation...of ..that coz in the next step we r drawing boundaries for ...the probability..... iam not able to connect between potential and probability... thank u
One way to visualize potential energy is like altitude on the surface of the Earth. Due to Earth's gravitational field, higher elevations have more potential energy. We can use this potential energy to run very fast down a hill, roll a ball, or build hydroelectric dams which power our homes.The steeper the slope, the more the force of gravity acts against us as we climb. The high the cliff, the more potential energy we have at the top. A jump from zero to infinite potential energy is like being at the bottom of a cliff that never ends. No matter what we do, we are stuck at the bottom and can't reach the top. Such is the case for the particle in a box. No matter what the particle does or how hard it tries, it will always remain stuck in the box, because it requries an infinite amount of energy to get out.
Hi Max. I'm not sure if I'd agree. There is a jump discontinuity in the potential energy at 0 and L, so I'm not sure if it's a well-defined quantity. Additionally, even if we choose to define a specific value at the boundaries, it is only so for an infinitesimal distance, which I don't think affects any observable properties in any quantifiable way. This is one of those nuances that mathematicians obsess about, but many physicists and most chemists don't give a second thought to en route through a derivation. If any viewer would like to choose a specific value of PE at the boundaries that's fine by me.
A normalized wave function integration over the complete room is 1 by definition which needs a upper and lower limit of L and 0 for the particle in the box concept thats why i found it confusing not to include 0 and L for the potential 0. good explanation anyway
Yes, it's a minor nuance over and open internal vs. a closed interval and whether the boundaries are considered to be part of the box. The limits of integration would be equivalent in either case. Either way, this matter of definitions is only relevant over an infinitesimally small region, and does not change the numerical values or their interpretation. This is the type of semantics that mathematicians tend to obsess over that physicists just gloss over without a second thought. I hadn't previously considered which comparison operators did or did not need "or equal to" signs underneath them, and it doesn't bother me if viewers differ in their choice of such.
that was my only "problem" witht this vid. I know that limits are same but you basicly said ) that V is inf. at x and l , ect. and than whan you are solving sys. of eq using boundry con. you say that Psi(0) =A=0. I think that for ppl who are learning , this might be little bit confusing, while if you include end points it makes more sence even for ppl who are not good with limits... but other than that great vid.
Hi Felis. Zero is not an acceptable value of n. In the case of zero, we have psi(x) = sqrt(2/L) * sin(0) = 0. Thus the wavefunction is zero at all possible values of x, thus we can't normalize the wavefunction and the probability of finding the particle anywhere is zero. This is called a "trivial solution" and is why zero is not an allowed value for the particle in a box.
Really good explanation but I'm lost on one thing. You said the particle doesn't have enough energy to leave the box, but isn't that valid only for macroscopic objects, and particles abruptly leave the box, hence making this a peculiar phenomenon that is characteristic of Quantum Mechanics?
The proper name for this model system is the infinite square well. In a truly infinite square well, particle escape is impossible, almost by definition. In order to escape, the particle would have to acquire an infinite amount of potential energy, and such an amount doesn't exist, as the total energy of the universe is finite and constant. The reason that particles can escape such situations in the real world is that no potential wall is truly infinite. Real systems are finite square wells, and particle may escape from finite square wells with sufficient energy. Finite square wells do display some weird quantum phenomena, but the limitation of finite vs. infinite square wells is not a matter of the weirdness of quantum mechanics but rather a practical limitation of our ability to construct such a system. The larger the potential barrier gets, the better the infinite square well model becomes as an approximation for such a system.
I think that problem is that tunneling occurs on barrier , you have no pot. barrier here and pot is defined as infinity everywhere except our little space, you cant tunnel through ininitely thic wall. I dont think you can calculate transmission coefficient since wave f. doesnt have any solutions in infinite potential, since it doesnt have any real physical meaning its like center of black hole ...
The goal of this video is to derive the allowed wavefunctions and energy levels of the particle in a box model system. This is a model for the properties of any sufficiently low-mass particle constrained in any sufficiently small space. It is the first example of this course of the origin of quantum behvaior due to the constraints of the position of the particle.
Due to the constraint of the particle's position to be inside the box, it now can't have any possible energy, momentum, etc. It can only have certain "quantized" values which are allowed by the Schrodinger equation. The solutions of the Schrodinger equation for the particle in a box happen to have an integer, "n", which tells us which states are allowed. This happens so that the wavefunction of the particle meets the "boundary conditions" we describe in this video, giving a physically reasonable result.
Thank you so much for the great explanation ! I live in Algeria and I'm a first year college student in industrial sciences. At the chemistry course they just tell us to skip the pure mathemetical part of quantum chemistry and simply apply it to quantum numbers and orbitals. I always wanted to truly get the math behind it, and your channel is exactly what I needed. Thank you again sir !
Thanks for sharing, Salim. Good luck as you continue in your studies. Your curiosity and willingness to dig deep to understand things beyond the expectations of your course work will prove very valuable as you progress in your career and life.
I came across your comment and was curious. How'd your studies go?
My material science prof decided not to go over this at all because "surely you've all already familiar with the Schrödinger equation", which we chemistry students, in fact, were not. So this was such a great and clear explanation of this model! Thank you!
Your explanation was fabulous. I've been struggling a bit with quantum chem at my uni and it made everything clear about the particle in a box. Thank you! Salutations from Brazil.
Glad to help out. Greetings from California.
I know it's been years, but I just came across your comment and was curious. How'd the rest of your class go?
@@PunmasterSTP It went great! I passed with an 8.5, if I recall correctly. I'm now doing my PhD in organic synthesis, and this knowledge is still extremely useful for me. Thanks again :)
@@rodrigogomes5950That's awesome you passed, and even more awesome that you're using your knowledge with what you're doing now! I hope your research continues to go well.
Absolutely brilliant, and you're answering every important question in the comments, what a good teacher. Thanks for all your work!
Thanks, Narice. Comments are where the magic happens.
I realize I am pretty randomly asking but does anyone know of a good site to watch newly released movies online?
@Axel Arjun Lately I have been using FlixZone. You can find it by googling =)
@Axel Arjun Lately I have been using Flixzone. You can find it on google :)
@Axel Arjun try Flixzone. You can find it on google =)
Your video are really helping me a lot in understanding quantum chemistry...
I got stuck on a video about the maxwell boltzmann distribution in a channel called tonya coffey (great channel by the way) because of this very concept of energy in different nodes of waves so i searched online in google and youtube i found this video which i will definitely share this with my quantum enthusiastic friends. Amazing video TMP
from India
its actually awesome that you reply to people in the comment section!
PIB? More like "Perfect videos for me!" Thanks for sharing.
On another note, the first time I saw this material I thought it was so cool that we could derive a "quantum number", after having seen them being described (but not derived) in gen chem.
This topic is crystal clear to me now... Thank you so much..
Outstanding elaboration. I wish You Tube was available back in 1988 when I first took QC course 🙄🙄
ruclips.net/video/HXEYnmTd2bs/видео.html
@ 2:35 Remember that 2.m.E = 2.m.(1/2.m.v^2) = m^2 . v^2 = p^2 . So k = p / h-bar !
@ 6:54 There is only 1 quantum-number here because this is a 1-dimensional situation.
Thank you so much for these. Revising for collections and these are so helpful!!!
Thank you for your effort! These videos have been of great help.
Thanks, Amr.
very clear explanation, thank you!
great job from egypt
Your explanation was much specific and clear than many of the Indian youtubers. Really grateful to find you on youtube.
Is there any more elegant way of finding the form of psi than by just guessing that it should be of the form Asinkx+Bcoskx and differentiating twice to find what k should be? I was looking for some way of finding that sin and cos form rather than just knowing it.
really nice and easy to understand videos.... all the conceptual doubts get cleared...
Glad to hear it's working as intended.
When you took x= l part why did you exclude the cosine part
Thankyou sir. I want to know if the boundaries of the well are -L/2 to L/2 , what will be the energy ?
In contrast to the normal wave equation whose solution is a linear combination of the eigenfunctions, here, because of quantization of energy, must the solution be only ONE of the eigenfunctions?
why have you taken an extra wave function in the Hamiltonian operator when simplifying H* wave function= E*wavefunction ?
Why we would need an operator "A" for Psy(x). At 2.01
Why there is an x in between Psy(x)
Psy(x) x Psy(x)
I don't understand the question.
@S R Thank you & My apologies, i must have been out of my mind. My comments were intended for the video "Quantum Chemistry 3.9 - Average Position" ruclips.net/video/sCeUFzxowuQ/видео.html
@@TMPChem Thank you & My apologies, i must have been out of my mind. My comments were intended for the video "Quantum Chemistry 3.9 - Average Position" ruclips.net/video/sCeUFzxowuQ/видео.html
I could not get why the more the length and the mass , the more the energy levels become closer?
Note: The very nature of reality is probably analog (interacting energy modalities). Now sure, digitizing an analog universe would allow an entity to accurately do stuff, but it still would not be how actual reality would actually be. Science has to get off of their 'particle mentality' to try to discern the actual Theory Of Everything. Currently, science is coming up with things like 'virtual particles' because they are stuck on a particle mentality. A virtual particle does not exist in actual reality, it's 'virtual'.
Edit: and likewise, an imaginary number 'i', is an imaginary number.
Excuse me. I don't understand the step of k = sqrt(2mE)/h bar. Why does d^2 psi(x)/dx^2 = - k^2 psi(x)?
Hi Jo. We are guessing a trial function for Psi(x) which is Acos(kx) + Bsin(kx). When we take the second derivative of this function, it can be factored into the form [ -k^2 (Acos(kx) + Bsin(kx)) ]. So we have a negative constant squared times Psi(x) is equal to the second derivative, just as our light blue equation requires. In order for these equations to be equal, -k^2 must be equal to -2mE / hbar^2, which we can solve for the value of k given in orange.
I really don't get the assumption of why V(x)=0... You are saying there is a box (with infinite height???) and as long as the particle remains between x and l (i.e. inside the box, since its impossible escape from the top which is infinitely high) it's potential energy is 0? I mean, first off how do you know anything at all about the potential energy(s) of the particle? What does the fact that its stuck in a box have to do with potential energy and what kind of potential energy are you talking about? The way you are saying it is like it has ZERO potential energy in the box no matter its interaction with the surrounding, its position or the forces acting on it.
Hi Adam. For the purposes of analysis of the system, it doesn't matter what the energy is inside the box, it just matters that whatever the energy is inside the box, it's the same everywhere, and the boundary is infinitely high so that the particle is incapable of escaping. Having a flat potential energy surface (PES) inside the box means that the derivative of the potential everywhere inside the box is zero, which means there is no force acting on the particle except for the walls, where an infinitely strong force keeps the particle inside the box.
We could just as easily define the energy inside the box to be 1, 2, or any other finite real number and the wavefunctions would be exactly the same, with the energy offset by the value we chose V(x) to be. Since this value is arbitrary, it is most convenient to choose that arbitrary value to be zero, which is why we've done that. As for why we know this, it's a model system and those are the parameters we've defined. They are true by definition. The usefulness of the model is how closely it corresponds to real systems to provide insight into their behavior.
Thank you!
Thank You 🙏🏻
Thanks Cyrille.
sir if v(x) = infintity.....means......could u pls give me little intimation...of ..that
coz in the next step we r drawing boundaries for ...the probability.....
iam not able to connect between potential and probability...
thank u
One way to visualize potential energy is like altitude on the surface of the Earth. Due to Earth's gravitational field, higher elevations have more potential energy. We can use this potential energy to run very fast down a hill, roll a ball, or build hydroelectric dams which power our homes.The steeper the slope, the more the force of gravity acts against us as we climb. The high the cliff, the more potential energy we have at the top. A jump from zero to infinite potential energy is like being at the bottom of a cliff that never ends. No matter what we do, we are stuck at the bottom and can't reach the top. Such is the case for the particle in a box. No matter what the particle does or how hard it tries, it will always remain stuck in the box, because it requries an infinite amount of energy to get out.
@@TMPChem That is some brilliant analogy! Thank you very much.
potential energy is also 0 for 0 and L
Hi Max. I'm not sure if I'd agree. There is a jump discontinuity in the potential energy at 0 and L, so I'm not sure if it's a well-defined quantity. Additionally, even if we choose to define a specific value at the boundaries, it is only so for an infinitesimal distance, which I don't think affects any observable properties in any quantifiable way. This is one of those nuances that mathematicians obsess about, but many physicists and most chemists don't give a second thought to en route through a derivation. If any viewer would like to choose a specific value of PE at the boundaries that's fine by me.
A normalized wave function integration over the complete room is 1 by definition which needs a upper and lower limit of L and 0 for the particle in the box concept thats why i found it confusing not to include 0 and L for the potential 0. good explanation anyway
Yes, it's a minor nuance over and open internal vs. a closed interval and whether the boundaries are considered to be part of the box. The limits of integration would be equivalent in either case. Either way, this matter of definitions is only relevant over an infinitesimally small region, and does not change the numerical values or their interpretation. This is the type of semantics that mathematicians tend to obsess over that physicists just gloss over without a second thought. I hadn't previously considered which comparison operators did or did not need "or equal to" signs underneath them, and it doesn't bother me if viewers differ in their choice of such.
that was my only "problem" witht this vid. I know that limits are same but you basicly said ) that V is inf. at x and l , ect. and than whan you are solving sys. of eq using boundry con. you say that Psi(0) =A=0. I think that for ppl who are learning , this might be little bit confusing, while if you include end points it makes more sence even for ppl who are not good with limits... but other than that great vid.
Can't n also be equal to 0? sin(n•pi)=sin(0•pi)=sin(0)=0.
It says that n can only be (1, 2, 3, 4, 5...), but there is no 0 in there.
Hi Felis. Zero is not an acceptable value of n. In the case of zero, we have psi(x) = sqrt(2/L) * sin(0) = 0. Thus the wavefunction is zero at all possible values of x, thus we can't normalize the wavefunction and the probability of finding the particle anywhere is zero. This is called a "trivial solution" and is why zero is not an allowed value for the particle in a box.
How did you get rid of pi at 7:06???
Hi Erica. We initially have hbar and pi in the numerator. hbar = h / pi, thus hbar * pi = h * pi / pi = h. The bar has been cancelled out.
Really good explanation but I'm lost on one thing. You said the particle doesn't have enough energy to leave the box, but isn't that valid only for macroscopic objects, and particles abruptly leave the box, hence making this a peculiar phenomenon that is characteristic of Quantum Mechanics?
The proper name for this model system is the infinite square well. In a truly infinite square well, particle escape is impossible, almost by definition. In order to escape, the particle would have to acquire an infinite amount of potential energy, and such an amount doesn't exist, as the total energy of the universe is finite and constant. The reason that particles can escape such situations in the real world is that no potential wall is truly infinite. Real systems are finite square wells, and particle may escape from finite square wells with sufficient energy. Finite square wells do display some weird quantum phenomena, but the limitation of finite vs. infinite square wells is not a matter of the weirdness of quantum mechanics but rather a practical limitation of our ability to construct such a system. The larger the potential barrier gets, the better the infinite square well model becomes as an approximation for such a system.
I think that problem is that tunneling occurs on barrier , you have no pot. barrier here and pot is defined as infinity everywhere except our little space, you cant tunnel through ininitely thic wall. I dont think you can calculate transmission coefficient since wave f. doesnt have any solutions in infinite potential, since it doesnt have any real physical meaning its like center of black hole ...
Sir pls tell what are we trying to find...pls reply its v urgent
The goal of this video is to derive the allowed wavefunctions and energy levels of the particle in a box model system. This is a model for the properties of any sufficiently low-mass particle constrained in any sufficiently small space. It is the first example of this course of the origin of quantum behvaior due to the constraints of the position of the particle.
looks like someone left this to the last minute before an exam!
and also sir...pls give the intimation of that................"n"....quantum no....!!!
Due to the constraint of the particle's position to be inside the box, it now can't have any possible energy, momentum, etc. It can only have certain "quantized" values which are allowed by the Schrodinger equation. The solutions of the Schrodinger equation for the particle in a box happen to have an integer, "n", which tells us which states are allowed. This happens so that the wavefunction of the particle meets the "boundary conditions" we describe in this video, giving a physically reasonable result.
America 🇺🇸 does all things nicely
Nobody's perfect.
Thank you ❤️!