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Why symmetric potential has even bound ground state and does odd ground state exist?

Physics Asked on September 25, 2021

I have read that symmetric potential has even bound ground state, but I don’t know how to derive it? The only conclusion I can derive is for even potential I can take real wavefunction.

I also want to ask, if odd bound ground state ever exist? I have never seen any.

One Answer

One particle wave function for a bound ground state does not have nodes. This is obviously not the case for the wave functions of several fermions, which necessarily have zeros to satisfy the Pauli principle. Note also that the wave functions of the eigenstates of a scalar potential can also always be chosen real.

Correct answer by Roger Vadim on September 25, 2021

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