CC fixes 10:47 if we are naive, the error in the phase 21:57 the phase is a little 21:59 the phase is 22:14 call the phase here 22:38 represents the phase 22:42 the phase Anywhere you have "face" should probably be "phase" 28:48 uncertainty in p and x 33:08 for t less than 38:56 it's a state 40:40 because they might evolve and the uncertainties will change 45:58 or so, "sinch" should be "sinh". Likely other places 50:24 "on it" is correct 51:44 hope for an exact solution 58:44 Am I in this lucky situation? 1:06:42 is the star of the 1:23:09 to the x position
Great lecture professor. Thank you for puting all of these online with the lecture notes and assignements. They've been of great use to further study QM while finishing my Bcahelor in Physics.
I like the concept of Squeeze States need to learn more about it. Very Nice lecture again. Thanks a lot , you have made the the math look much much comprehensible. I loved all your lectures so far so I went ahead and bought the Book with you as the author. Hope I read atleast parts of it , just not sit on my book shelf. You have really sparked a lot of interest in me in Quantum Mechanics. I am retired Aerospace/ Mechanical Engineer. It was interesting also. We need more teachers like you.
At 25:00 - "I expect the position to be in the interval +/- delta-x." That doesn't mean anything unless you associate a probability with it. The measurement will fall in that range some fraction of the time - it will fall in a larger range some larger fraction of the time. Even if he's tacitly implying "more than half the time" he should say so. Also, that length he used to compute the phase uncertainty is not 1 - it is 1/2. That blob is a *circle*, and both of the other diameters he assessed he measured in at 1/2, so that one needs to be 1/2 as well. That makes the phase uncertainty 1/2, just like the position and momentum uncertainty.
you're insisting on being extremely technical in your analysis and in that regard you're right. However, the professor had in an earlier lecture already said that his approach was only to be 'reasonably' rigorous and he was not going to be completely precise and formal. The mathematics is too hard to obtain analytical solutions and good approximations teach us a lot of the physical situation. Also about the second point you made, the energy-time uncertainty, and the phase-number uncertainty that is derived from it is not an equality, it just says its in the order of that number. so saying 1/2 and 1 is somewhat the same. You mean its some number around 1ish.
can someone provide a justification to why prof zweibach wrote the gs of the harmonic oscillator with respect to the first (original ) hamiltonian as a superposition of the ground state of the same oscillator but being under the influence of the second hamiltonian ?
@40:12, does he means that the changing of H/mass/w will not influence the wavefunction immediately?? It needs some time to form a new wave function?? Is that right??? Why possible?
Yes, the wave-function is not effected immediately by change of the Hamiltonian. Here the Gaussian wave-function represents the ground state of the first Hamiltonian. But changing the Hamiltonian, the Gaussian wave-function has to undergo a time evolution to become suitable (say an energy eigen state) for the second Hamiltonian. The process takes some finite time. Consider a viscous liquid for example, you can change the dimensions of the vessel holding the liquid immediately by some means but the fluid will take a finite time to acquire the shape of the new container.
CC fixes
10:47 if we are naive, the error in the phase
21:57 the phase is a little
21:59 the phase is
22:14 call the phase here
22:38 represents the phase
22:42 the phase
Anywhere you have "face" should probably be "phase"
28:48 uncertainty in p and x
33:08 for t less than
38:56 it's a state
40:40 because they might evolve and the uncertainties will change
45:58 or so, "sinch" should be "sinh". Likely other places
50:24 "on it" is correct
51:44 hope for an exact solution
58:44 Am I in this lucky situation?
1:06:42 is the star of the
1:23:09 to the x position
Thanks for your time and effort! All changes have been done to the caption.
Great lecture professor. Thank you for puting all of these online with the lecture notes and assignements. They've been of great use to further study QM while finishing my Bcahelor in Physics.
I like the concept of Squeeze States need to learn more about it. Very Nice lecture again. Thanks a lot , you have made the the math look much much comprehensible. I loved all your lectures so far so I went ahead and bought the Book with you as the author. Hope I read atleast parts of it , just not sit on my book shelf.
You have really sparked a lot of interest in me in Quantum Mechanics. I am retired Aerospace/ Mechanical Engineer. It was interesting also.
We need more teachers like you.
the claps at the end of lectures are truly phenomenol,
Thanks ❤️🤍
At 25:00 - "I expect the position to be in the interval +/- delta-x." That doesn't mean anything unless you associate a probability with it. The measurement will fall in that range some fraction of the time - it will fall in a larger range some larger fraction of the time. Even if he's tacitly implying "more than half the time" he should say so.
Also, that length he used to compute the phase uncertainty is not 1 - it is 1/2. That blob is a *circle*, and both of the other diameters he assessed he measured in at 1/2, so that one needs to be 1/2 as well. That makes the phase uncertainty 1/2, just like the position and momentum uncertainty.
you're insisting on being extremely technical in your analysis and in that regard you're right. However, the professor had in an earlier lecture already said that his approach was only to be 'reasonably' rigorous and he was not going to be completely precise and formal. The mathematics is too hard to obtain analytical solutions and good approximations teach us a lot of the physical situation. Also about the second point you made, the energy-time uncertainty, and the phase-number uncertainty that is derived from it is not an equality, it just says its in the order of that number. so saying 1/2 and 1 is somewhat the same. You mean its some number around 1ish.
can someone provide a justification to why prof zweibach wrote the gs of the harmonic oscillator with respect to the first (original ) hamiltonian as a superposition of the ground state of the same oscillator but being under the influence of the second hamiltonian ?
@40:12, does he means that the changing of H/mass/w will not influence the wavefunction immediately?? It needs some time to form a new wave function?? Is that right??? Why possible?
Yes, the wave-function is not effected immediately by change of the Hamiltonian. Here the Gaussian wave-function represents the ground state of the first Hamiltonian. But changing the Hamiltonian, the Gaussian wave-function has to undergo a time evolution to become suitable (say an energy eigen state) for the second Hamiltonian. The process takes some finite time.
Consider a viscous liquid for example, you can change the dimensions of the vessel holding the liquid immediately by some means but the fluid will take a finite time to acquire the shape of the new container.
@@vedantkashyap5703 that's a good way to explain it. Thank you!
@@mississippijohnfahey7175 You're welcome 🤗
1:14:12 Does anyone know where I can find the proof of the squeeze operator that Professor mentioned here?
Today I see the power of mathematics 🤯🤯
I don't know why
Me neither...