Okay, it makes sense that x^2 would have a non-zero expectation value as you would end up with even integrals. I took a different approach as I thought we were looking for a combination of wave functions for which x would be non-zero, so I went with Psi = Psi_2 + Psi_3, which will also give you those even integrals we'd be looking for, and I believe turns out to be a time dependent wave function that oscillates sinusoidally. Is such a combination possible? Do we need the ground state to be part of the wave function? I wouldn't think we would, but I actually don't know.
Okay, it makes sense that x^2 would have a non-zero expectation value as you would end up with even integrals. I took a different approach as I thought we were looking for a combination of wave functions for which x would be non-zero, so I went with Psi = Psi_2 + Psi_3, which will also give you those even integrals we'd be looking for, and I believe turns out to be a time dependent wave function that oscillates sinusoidally. Is such a combination possible? Do we need the ground state to be part of the wave function? I wouldn't think we would, but I actually don't know.
ReplyDeleteWhat you did is totally reasonable. such a combination is possible. The problem you created is totally fine and interesting.
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