Ch 4 The quantum system with potential $V(x) = \frac{1}{2}m\omega^2 x^2$. Energy levels are $E_n = (n + \frac{1}{2})\hbar\omega$, equally spaced with zero-point energy $E_0 = \frac{1}{2}\hbar\omega$. The most important exactly solvable problem in quantum mechanics due to its universality near any po