GR0177 #94


Problem


This problem is still being typed. 
Quantum Mechanics}Perturbation Theory
The energy for firstorder perturbation theory of ( is the known Hamiltonian and is the perturbed Hamiltonian) is given by , where the wavefunctions are the unperturbed ones.
Thus, the problem amounts to calculating . This is just raising and lowering operator mechanics.
. But, after braketting, one finds that the expectation value of and are 0, since and , are orthogonal. Thus, the problem becomes,
. Applying the given eigenequations, one finds that . For , one finds , as in choice (E).
(Note that: and and .)


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Comments 
sjayne 20150623 11:22:35  I did it the same way. a ended up being 1> and adagger was 3> . Foiling it out any of the terms where 1> and 3> multiply go to 0, and in any of the terms where the kets are the same the kets go to 1. So you are left with V(2+3)=5V   risyou 20121107 22:49:18  It just looks like the harmonic oscillator if you have tried to express them with the up down operator.
So I just put n=2 to it.. no answer so I give it up.
I feel so tried after doing 70+ question.   Donofnothing 20101008 12:04:06  this doesn't make much sense. I got the same answer from facotring out the (a+adagger) term, ignoring the (a*adagger), and using only a^2 and a^dagger squared. did i just get lucky, or is this alternate?
keradeek 20110826 01:03:37 
yeah, you just got super lucky.

FutureDrSteve 20111104 17:34:55 
Awesome! My plan is to get lucky on 100 problems in a row.... :S

yummyhat 20171027 05:19:08 
same\r\n

 

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