GR0177 #94
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Problem
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This problem is still being typed. |
Quantum Mechanics}Perturbation Theory
The energy for first-order perturbation theory of ( is the known Hamiltonian and is the perturbed Hamiltonian) is given by , where the wave-functions are the unperturbed ones.
Thus, the problem amounts to calculating . This is just raising and lowering operator mechanics.
. But, after bra-ketting, one finds that the expectation value of and are 0, since and , are orthogonal. Thus, the problem becomes,
. Applying the given eigen-equations, one finds that . For , one finds , as in choice (E).
(Note that: and and .)
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Alternate Solutions |
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Comments |
sjayne 2015-06-23 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 2012-11-07 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 2010-10-08 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 2011-08-26 01:03:37 |
yeah, you just got super lucky.
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FutureDrSteve 2011-11-04 17:34:55 |
Awesome! My plan is to get lucky on 100 problems in a row.... :S
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yummyhat 2017-10-27 05:19:08 |
same\r\n
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