Symmetric potential

for a symmetrical potential with one electron, i know that the wavefunctions are symmetric or antisymmetric. for the ground state why is the wavefunction symmetric?

Also, if you add a second electron that is non-interacting, (why) does it have the same wavefunction as the first electron?

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Physics Monkey
Homework Helper
I assume we are talking 1d here? So you've solved the 1d Schrodinger equation and have obtained the bound states of the system, right? You've put your first electron into the ground state, now what is the lowest energy single particle state available to the next electron? (Hint: the electron has spin 1/2)

Physics Monkey said:
I assume we are talking 1d here? So you've solved the 1d Schrodinger equation and have obtained the bound states of the system, right? You've put your first electron into the ground state, now what is the lowest energy single particle state available to the next electron? (Hint: the electron has spin 1/2)

Yes, the problem is in 1-D. The potential is a general symmetric potential, so we don't know necessarily have an actual analytical solution to Schrodinger equation. So how do we know the ground state must be symmetric, and that if we put another electron in the potential, it has the same wave function?

CarlB