Hi guys, I'm reading Shankar and he's talking about the Variational method for approximating wave functions and energy levels.(adsbygoogle = window.adsbygoogle || []).push({});

At one point he's using the example [itex]V(x) = λx^4[/itex], which is obviously an even function. He says "because H is parity invariant, the states will occur with alternating parity".

I believe him because I remember this from the Harmonic oscillator and the infinite square well, and I see why in each of those examples they alternate, from a mathematical standpoint.

But is there a better physical explanation? Right now all I can really tell is, mathematically, for those two examples, the solutions have to have alternating parity. So how can he say this for sure of all even potentials?

Thanks!

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# Parity switching wave functions for a parity invariant hamiltonian?

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