I never learned this in the lectures (maybe I was sleeping), but now I think I finally realized what is the reason that eigenstate solutions of SE with a symmetric potential are either symmetric or antisymmetric. Is the argument this:(adsbygoogle = window.adsbygoogle || []).push({});

"The Hamiltonian and the space reflection operator commute, therefore they have common eigenstates" ?

If it is this, can somebody explain me why does a constant potential (which is also symmetric) have plane wave solutions, that are not symmetric or antisymmetric.

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# Symmetric potential

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