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!

Harmonic oscillator

  1. Dec 4, 2005 #1
    why is the lowest allowed energy not E=0 but some definite minimum E=E0?
  2. jcsd
  3. Dec 4, 2005 #2


    User Avatar
    Homework Helper
    Gold Member

    If you solve the Time Independent Schrodinger equation for the Harmonic Oscillator, that is
    [tex] -\frac{\hbar^2}{2m} \frac{d^2\Psi}{dx^2} + \frac{1}{2}kx^2 \Psi = E \Psi [/tex]

    The quantization of energy comes from the boundary conditions (ie, [itex] \Psi = 0 [/itex] when [itex] x= \infty [/itex] or [itex] x = -\infty [/itex]).

    The permitted energy levels will be

    [tex] E_n = (n+\frac{1}{2}) \hbar \omega [/tex]

    So the lowest Energy is not E=0.
    Last edited: Dec 4, 2005
  4. Dec 4, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper

    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.
  5. Dec 4, 2005 #4
    thank you very much!!! :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Harmonic oscillator
  1. Harmonic Oscillator (Replies: 2)

  2. Harmonic oscillator (Replies: 9)

  3. Harmonic Oscillator (Replies: 1)

  4. Harmonic oscillator (Replies: 1)

  5. Harmonic oscillator (Replies: 1)