# Harmonic oscillator

by asdf1
Tags: harmonic, oscillator
 HW Helper PF Gold P: 1,198 If you solve the Time Independent Schrodinger equation for the Harmonic Oscillator, that is $$-\frac{\hbar^2}{2m} \frac{d^2\Psi}{dx^2} + \frac{1}{2}kx^2 \Psi = E \Psi$$ The quantization of energy comes from the boundary conditions (ie, $\Psi = 0$ when $x= \infty$ or $x = -\infty$). The permitted energy levels will be $$E_n = (n+\frac{1}{2}) \hbar \omega$$ So the lowest Energy is not E=0.