# Momentum of 1d harmonic oscillator

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1. Oct 17, 2015

### ambroochi

The ground state wave-function of a 1-D harmonic oscillator is
$$\psi(x) = \sqrt\frac{a}{\sqrt\pi} * exp(-\frac{a^2*x^2}{2}\frac{i\omega t}{2}).$$
a) find Average potential energy ?
$$\overline{V} = \frac{1}{2} \mu\omega^2\overline{x^2}$$
b) find Average kinetic energy ?
$$\overline{T} = \frac {\overline{p^2}}{2\mu}$$

c) find momentum probability function ?

solving for a i got the answer as
$$V=\frac{1}{4}\hbar\omega$$

how do i find the momentum here ?

Last edited: Oct 17, 2015
2. Oct 17, 2015

### BvU

Hello Ambroochi. Welcome to PF !

That is all very nice, but what is your question ? And oh, perhaps you want to read the PF guidelines first. You will get much better assistance when you adhere to them !