How do we go from the operator exponential involving p-hat^2 to the exponential involving the eigenvalue p^2? Is this by taking the definition of the operator exponential as it's power series expansion of operators, then acting term by term on |p>?
There are two ways to do it: (1) use Taylors' expansion of the exponential and apply the operator powers to the momentum eigenket or (2) (easier) remember the theorem that if \hat{A}|a>=a|a> then for any function we have f(\hat{A})|a>=f(a)|a>
Fantastic exposition. Thanks!
Glad you enjoyed it!
Very interesting! Congrats!
@ 7:20 This is NOT time-evolution. This is propagation in time AND space.
@ 8:39 How can a iime-evolution operator U change the position???
This video is a wonderful symphony comparable to all cosmic music
Thank you from the heart, thank you very much
Explained very well. Thank you!!
Glad it was helpful!
Great video!
Very good video!
This video is wonderful
thank you for explaining this complex topic so patiently
How do we go from the operator exponential involving p-hat^2 to the exponential involving the eigenvalue p^2? Is this by taking the definition of the operator exponential as it's power series expansion of operators, then acting term by term on |p>?
There are two ways to do it: (1) use Taylors' expansion of the exponential and apply the operator powers to the momentum eigenket or (2) (easier) remember the theorem that if \hat{A}|a>=a|a> then for any function we have f(\hat{A})|a>=f(a)|a>
Sir can you give us lecture on path integral calculation for forced and coupled quantum harmonic oscillators
I do not have one recorded at this point but I will post one if I get the time to make it!
@@vincentmeunier7873 Sir, these videos are very helpful, but I cannot find the rest of these since the playlist has not been made.
The playlist if complete; I currently have four playlists on my channel. Check them out!
what is the book that you used?
As far as I can tell, this is the derivation from Chap 8 of Townsend.
Townsend
Very very nice explanation
Where I can find more videos for u ?
Really amazing lecture
❤️❤️
🦄