## harmonic oscillator

why is the lowest allowed energy not E=0 but some definite minimum E=E0?
 Recognitions: Gold Member Homework Help 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.
 Recognitions: Homework Help Science Advisor I could give a hand-wave argument. We have E=1/2mv^2+1/2kx^2. If E=0 both x and v are zero, which contradicts Heisenberg.

## harmonic oscillator

thank you very much!!! :)