- #1
teroenza
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Homework Statement
I am trying to follow Sakurai's use of perturbation theory on a harmonic oscillator,
Homework Equations
Perturbation:
[tex]v=\epsilon x^2[/tex] , [tex]\epsilon << 1 [/tex]
Matrix elements:
[tex] V_{km}=<k|v|m> [/tex]
The Attempt at a Solution
The book says that all other matrix elements besides [itex]V_{00}, V_{20} [/itex], and of the form [itex] V_{k0}=<k|v|0> [/itex] vanish. I don't understand why. I see that the perturbation and the ground state have even parity, and that the SHO eigenstates alternate between even and odd parity with quantum number n. That should kill off the odd n states, but why should the even ones vanish too for k above 2?