Using symmetry solving Schrödinger equation

[Pifagor]

Homework Statement

When solving, say, the double delta function potential well, we fix constants using continuity. If the potential is symmetrical about the origin, can we conclude that the wave function, i.e. the solution, will also be symmetric? I found this way made the calculations much easier, but is it correct?

 

[TSny]

If the potential is symmetric about the origin then the non-degenerate stationary states will either be symmetric or antisymmetric about the origin. For example, for a particle in a 1D infinite well the states alternate between symmetric and antisymmetric as you go up the energy ladder.

 

[Pifagor]

Thanks!