1. Limited time only! Sign up for a free 30min personal 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!

Harmonic oscillator

  1. Aug 21, 2014 #1
    1. The problem statement, all variables and given/known data

    A harmonic oscillator of mass m and angular frequency ω experiences the potential:

    V(x) = 1/2m[itex]ω^{2}x^{2}[/itex] between -infinity < x < +infinity


    and solving the schrodinger equation for this potential yields the energy levels

    E_n = (n + 1/2) h_bar ω


    Determine the energy levels for the half oscillator for which

    V(x) = 1/2m[itex]ω^{2}x^{2}[/itex] between -infinity < x < 0

    = infinity otherwise



    3. The attempt at a solution



    -h_bar^2/2m *d^2ψ(x)/dx^2 + 1/2mω^2x^2 = Eψ(x)


    so d^2ψ(x)/dx^2 = -(E - 1/2mω^2x^2)*2m/h_bar^2 ψ(x) ==> d^2ψ(x)/dx^2 = k^2ψ(x)



    So the general solution is ψ(x) = Ae^kx + Be^-kx
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 21, 2014 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Your k is not constant and generally depends on x, which means your differential equation is more difficult than that to solve.

    The fact that you have been given the energy levels for the full oscillator should be a hint. Can you think of a way to relate the problem of the half-oscillator to the full oscillator?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Harmonic oscillator
  1. Harmonic Oscillator (Replies: 5)

  2. Harmonic Oscillator (Replies: 12)

  3. Harmonic Oscillator (Replies: 3)

  4. Harmonic Oscillator (Replies: 3)

  5. Harmonic Oscillators (Replies: 3)

Loading...