Question

Is it possible to create a quantum state in which one electron in an infinite square-well potential is in the n = 2 state with spin up and another electron is in the ground state (n = 1) with spin up?

If so, write it out and make sure that it is antisymmetric. If not, explain why not.

Answer 1

Yes, it is possible because, it doesn't violate the pauli exclusion principle, as the two electrons are not confined to the same state.

Since the electrons are fermions, the wave function must be anti symmetric. The wave function is the product of special wave function and the spin wave function.

Since the spin wave function is symmetric, the space wave function must be anti symmetric so as to make the total wave function anti symmetric