Excellent Explantion! Such explanations were not explained with such mind blowing graphical stuffs in any of the popular books I read. A Must watch for every Quantum Physics Students.
The state is scattering if E>V(-inf)..... Scattering state basically tells us that the wavefunction extends upto infinity and is not non normalizable... hence we require Fourier transform and other trcks to superpose the wavefunctions and get a sensible wavefunction describing a particle
@@sayanmondal4570 Not really, you don't require Fourier transforms just because it's a scattering state. The Fourier transform is also useful for the particle in a box, which is a bound state.
That's really interesting. So does that mean that properties of the universe outside a potential well do NOT display quantum effects? Does this also mean that angular momentum is not quantized at energies well above the potential, etc.? Also, what about quantization of the the EM and gravity field way out in intergalactic space? If there's ostensibly no EM or gravitational potential fields out there, does any quantum behavior exist? I thought that the loop quantum gravity guys, etc,, were trying to build their model on quantizing the gravitational field.
The properties of the universe outside a potential well still display quantum effects -- the scattering states are still described by wavefunctions, after all, so they still exhibit uncertainty, wave/particle duality, etc. By "quantum effects", people generally mean more than just quantization of the energy levels. As for angular momentum, I can't say much here since this video was only talking about a 1-d quantum system and you can't have angular momentum in one dimension, but suffice it to say that angular momentum (for example of two masses stuck together by a rod) is quantized even if the object is floating off in the blackness of space. As for quantization of the EM and gravitational fields in intergalactic space, you're rapidly getting out of my area of expertise, so you'll have to continue to a treatment of relativistic quantum mechanics and/or quantum field theory to get a good answer for how the electromagnetic field is quantized. The short answer is that while there won't be a "potential" as described in this video and thus the energy of a single particle might not be quantized, the energy of the overall electromagnetic field comes from an ensemble of particles, and the number of particles has to be an integer, so you still have a quantized system, counting particles at a variety of energies instead of counting energy levels of a single particle.
I think that the explanation of "scattering states" is a bit lacking in clarity. Tunneling is Ok, and to be expected from all the previous videos and concepts. I haven't got the knack of the concept of quantum scattering (nor the relationship to the ordinary meaning of the word).
If you profesor or anyone watches my comment then kindly spare 1 minute or a half in answering that. I am following your Lectures religiously I got 2 questions for you professor 1. Are your videos uploaded in sequential manner. ? 2). Which textbook you would recommend as a freshman to quantum mechanics? I will be extremely grateful towards you
Dear sir, at the time 15:32, what is the difference between QHO bound state and the given second example on scattering state? I found both of them identical though! Can you please help me out? TIA
this is a great lecture but i have one question in the lecture on infinite square well you said the wavefunction must be zero at the boundary conditions but in this lecture you say the wavefunction gradually approaches the zero value only after the boundary conditions. i am very confused? please help!!!!
It must be zero at the boundary because it's an infinite square well, i.e., the particle would have to have an infinite amount of energy to get through the infinite potential. In this case, it is a finite well, and the particle can get through the barrier with a finite amount of energy, even if it is less than the potential, which is due to tunneling.
In most of these graphs (such as the ones describing the quantum behavior), would it have not been more accurate to call the y-axis E for total energy instead of V(x)? I am prabably just misunderstanding...
i am struggling to understand the energies and behaviour at E1 and E2, as at some parts of the video , a particle was able to "tunnel through" to the other side without having the necessary energy required... or maybe i simply misunderstood. anyone willing to explain please?
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Excellent Explantion! Such explanations were not explained with such mind blowing graphical stuffs in any of the popular books I read. A Must watch for every Quantum Physics Students.
The best lecture in quantum mechanics...
three years later and still the best
four years later and still the best
five years later and still the best
8 years later and still the best
9 years later and still the best
Thank you for all of your videos
*Bound* *State* Trapped particle.
*Scattering* *State* If E > V(x) when x→+∞ or x→ -∞.
E₁ (Bound State)
E₂ (Scattering State)
E₃ (Scattering State)
Thanks for your explanation, really hope you well
You're so good!
K
E1: bound state
E2: scattering state since E>V(-inf)
E3: free particle/scattering??
how can you deduce that?? I coudnt understand the scattering state at all :(
The state is scattering if E>V(-inf)..... Scattering state basically tells us that the wavefunction extends upto infinity and is not non normalizable... hence we require Fourier transform and other trcks to superpose the wavefunctions and get a sensible wavefunction describing a particle
How can E3 be scattering state ? It looks all free.
@@sayanmondal4570 Not really, you don't require Fourier transforms just because it's a scattering state. The Fourier transform is also useful for the particle in a box, which is a bound state.
Thank you sir
Great sir
Found this channel from a rhcp guitar cover, interesting
3:25 Kittenic energy? I prefer the Pupperic energy, myself 🙂 (But only if it's a Smol amount of Pupperic energy).
That's really interesting. So does that mean that properties of the universe outside a potential well do NOT display quantum effects? Does this also mean that angular momentum is not quantized at energies well above the potential, etc.? Also, what about quantization of the the EM and gravity field way out in intergalactic space? If there's ostensibly no EM or gravitational potential fields out there, does any quantum behavior exist? I thought that the loop quantum gravity guys, etc,, were trying to build their model on quantizing the gravitational field.
The properties of the universe outside a potential well still display quantum effects -- the scattering states are still described by wavefunctions, after all, so they still exhibit uncertainty, wave/particle duality, etc. By "quantum effects", people generally mean more than just quantization of the energy levels. As for angular momentum, I can't say much here since this video was only talking about a 1-d quantum system and you can't have angular momentum in one dimension, but suffice it to say that angular momentum (for example of two masses stuck together by a rod) is quantized even if the object is floating off in the blackness of space.
As for quantization of the EM and gravitational fields in intergalactic space, you're rapidly getting out of my area of expertise, so you'll have to continue to a treatment of relativistic quantum mechanics and/or quantum field theory to get a good answer for how the electromagnetic field is quantized. The short answer is that while there won't be a "potential" as described in this video and thus the energy of a single particle might not be quantized, the energy of the overall electromagnetic field comes from an ensemble of particles, and the number of particles has to be an integer, so you still have a quantized system, counting particles at a variety of energies instead of counting energy levels of a single particle.
Bound state is confined with in one region,how can we take the equations in other region for E
I'd say:
E1 bound
E2 scattering
E3 scattering
This was a cool video, but I just have a question: what if we have a bound state (so E
when the wave function blows up/down it is no more in the Hilbert space as the function won't be square integrable. right ?
I think that the explanation of "scattering states" is a bit lacking in clarity. Tunneling is Ok, and to be expected from all the previous videos and concepts. I haven't got the knack of the concept of quantum scattering (nor the relationship to the ordinary meaning of the word).
If you profesor or anyone watches my comment then kindly spare 1 minute or a half in answering that. I am following your Lectures religiously I got 2 questions for you professor 1. Are your videos uploaded in sequential manner. ? 2). Which textbook you would recommend as a freshman to quantum mechanics? I will be extremely grateful towards you
These lectures follow Griffiths QM, and they are ordered sequentially according to that book.
@@hershyfishman2929 but he haven't thought parity operator time dependent perturbation theory wkb principal
@@abhinandanmehra7765 indeed those are not in Griffiths book up until here
Dear sir, at the time 15:32, what is the difference between QHO bound state and the given second example on scattering state? I found both of them identical though! Can you please help me out? TIA
this is a great lecture but i have one question in the lecture on infinite square well you said the wavefunction must be zero at the boundary conditions but in this lecture you say the wavefunction gradually approaches the zero value only after the boundary conditions. i am very confused? please help!!!!
It must be zero at the boundary because it's an infinite square well, i.e., the particle would have to have an infinite amount of energy to get through the infinite potential. In this case, it is a finite well, and the particle can get through the barrier with a finite amount of energy, even if it is less than the potential, which is due to tunneling.
thanks that helped
In most of these graphs (such as the ones describing the quantum behavior), would it have not been more accurate to call the y-axis E for total energy instead of V(x)? I am prabably just misunderstanding...
is V(x) potential or potential energy? this is so confusing
yes
Potential is potential energy per unit
it is potential energy.
Potential energy function
i am struggling to understand the energies and behaviour at E1 and E2, as at some parts of the video , a particle was able to "tunnel through" to the other side without having the necessary energy required... or maybe i simply misunderstood. anyone willing to explain please?
Yes because if it's a quantum particle, the wave function is non zero at the region when E