Quantum hamonic oscillator half space potential

[YZer]

I'm trying to figure out what happens to the energy eigenstates when the quantum harmonic oscillator potential is over [0..infinity] rather then
[-infinity..infinity]. Originaly its hw(n +1/2)...

Thanks

[zefram_c]

Well, any even solution of the (-inf,inf) domain is no longer acceptable, but all odd solutions are still OK (properly renormalized). So I think the new ground state would be the 1st excited state of the old problem; and you'll have to figure out how to renormalize the wavefcn, but the energy eigenvalue should be the same.