1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A Shifted Harmonic Oscillator

  1. Mar 18, 2006 #1
    I have a wave function which is the ground state of a harmonic oscillator (potential centered at x=0)... but shifted by a constant along the position axis (ie. (x-b) instead of x in the exponential).

    How does this decompose into eigenfunctions?!?! I know it's an infinite sum... but I can't nail the coefficients.

    ...and...
    without knowing the decomposition, how can I get the time development of the average position and momentum???

    Help.

    Thanks.
     
  2. jcsd
  3. Mar 23, 2006 #2

    dextercioby

    User Avatar
    Science Advisor
    Homework Helper

    What does [itex] \exp\left[-(x-a)^{2}\right] [/itex] instead of [itex] \exp\left(-x^{2}\right) [/itex] have to do with time dependence of [itex] \langle \hat{x}\rangle [/itex]...?


    Daniel.
     
  4. Mar 24, 2006 #3
    Well, most intuitively, I would assume that shifting the initial wavefunction along the x axis would affect average position.

    Less intuitively, a shifted initial wavefunction in a zero-centered harmonic potential MUST be composed of eigenfunctions... ones centered at zero. Each of these have their own energies and own time development.

    As an example... go to THIS applet http://groups.physics.umn.edu/demo/applets/qm1d/index.html
    set it to harmonic oscillator, choose the ground state eigenfunction, and then adjust the offset.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A Shifted Harmonic Oscillator
  1. Harmonic Oscillator (Replies: 12)

  2. Harmonic Oscillator (Replies: 3)

  3. Harmonic Oscillator (Replies: 3)

  4. Harmonic Oscillators (Replies: 3)

  5. Harmonic oscillator (Replies: 1)

Loading...