hey there, great video. I am a physics student and am currently learning quantum mechanics. At 31:51 you said let's show that the eigenvalues are in fact hbar/2 and proceeded to show it through taylor series. You also said that since we got some phase in front of |+z> that it our assumption of hbar/2 eigenvalues must be correct but we would have gotten a phase in front of the + z ket for any integer multiple of hbar. Why would hbar/2 be the correct value then?
Ah good question that many students ask! The phase factor does NOT affect the eigenvalue at all! To convince yourself, write a simple eigenvalue problem and see the effect of an overall phase on BOTH the left and the right of the equation. Does that make sense?
This shows that we drop all the terms of order d\phi^2 and higher power. This is typical: you can think about d\phi being "as small as it gets without being zero", than its square can be neglected.
This video was SO clear and helpful. Thank you!
YOU ARE AMAZING!
hey there, great video. I am a physics student and am currently learning quantum mechanics. At 31:51 you said let's show that the eigenvalues are in fact hbar/2 and proceeded to show it through taylor series. You also said that since we got some phase in front of |+z> that it our assumption of hbar/2 eigenvalues must be correct but we would have gotten a phase in front of the + z ket for any integer multiple of hbar. Why would hbar/2 be the correct value then?
Ah good question that many students ask! The phase factor does NOT affect the eigenvalue at all! To convince yourself, write a simple eigenvalue problem and see the effect of an overall phase on BOTH the left and the right of the equation. Does that make sense?
14:29 thanks
Sorry, but at 24:07, where did the O(d*phi^2) come from?
This shows that we drop all the terms of order d\phi^2 and higher power. This is typical: you can think about d\phi being "as small as it gets without being zero", than its square can be neglected.
@@vincentmeunier7873 I see. Thanks
At around 1:08:00 I believe that the S matrix is written incorrectly
I do not believe so. What would you use instead?