- #1

- 72

- 1

This is more of a conceptual question and I have not had the knowledge to solve it.

We're given a modified quantum harmonic oscillator. Its hamiltonian is

H=[itex]\frac{P^{2}}{2m}[/itex]+V(x)

where V(x)=[itex]\frac{1}{2}[/itex]m[itex]\omega^{2}x^{2}[/itex] for x[itex]\geq[/itex]0 and V(x)=[itex]\infty[/itex] otherwise.

I'm asked to justify in terms of the parity of the quantum problem eigenfunctions why only odd integers n are allowed for the eigenenergies of the problem E=(n+1/2)[itex]\hbar\omega[/itex]

I have not a clue... well... actually my best guess was that the given potential impose the condition that the wavefunction is zero at x=0 and this is only the case for the odd ones. I'm confident about it but I could not find a problem like this anywhere to check my answer.

Thank you.

We're given a modified quantum harmonic oscillator. Its hamiltonian is

H=[itex]\frac{P^{2}}{2m}[/itex]+V(x)

where V(x)=[itex]\frac{1}{2}[/itex]m[itex]\omega^{2}x^{2}[/itex] for x[itex]\geq[/itex]0 and V(x)=[itex]\infty[/itex] otherwise.

I'm asked to justify in terms of the parity of the quantum problem eigenfunctions why only odd integers n are allowed for the eigenenergies of the problem E=(n+1/2)[itex]\hbar\omega[/itex]

I have not a clue... well... actually my best guess was that the given potential impose the condition that the wavefunction is zero at x=0 and this is only the case for the odd ones. I'm confident about it but I could not find a problem like this anywhere to check my answer.

Thank you.

Last edited: