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Momentum of 1d harmonic oscillator

  1. Oct 17, 2015 #1
    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. jcsd
  3. Oct 17, 2015 #2

    BvU

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    Science Advisor
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    Hello Ambroochi. Welcome to PF :smile: !

    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 !
     
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