Recent content by Patrick McBride

Cool, thanks for the explanation really helped out.

Ok so I had a crack at it and this is what I've gotten: ## \frac{P^2}{2m} +\frac{1}{2}kx^2 =H ## Harmonic Oscillator Hamiltonian ## -\frac{\hbar^2}{2m} \frac{d^2\Psi }{dx^2}+\frac{1}{2}kx^2 \Psi = E \Psi ## Schrödinger Equation for energy eigenstates. ## \omega =\sqrt{\frac{k}{m}} ## Replace...

Homework Statement Show that for the one-dimensional linear harmonic oscillator the Hamiltonian is: [; H = \frac{1}{2}[P^2+\omega ^2 X^2]-\frac{1}{2}\omega \hbar ;] [; =\frac{1}{2}[P+i\omega X][P-i\omega X]+\frac{1}{2} \omega \hbar ;] where P, X are the momentum and position operators...