# Harmonic oscillator

by asdf1
Tags: harmonic, oscillator
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 P: 741 why is the lowest allowed energy not E=0 but some definite minimum E=E0?
 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.
 Sci Advisor HW Helper P: 2,002 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.
 P: 741 Harmonic oscillator thank you very much!!! :)

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