Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quantum SHO Wave Functions not Complex?

  1. Aug 15, 2010 #1


    User Avatar
    Gold Member

    The Hermite Polynomials are solutions to the Schrödinger equation for the Quantum Simple Harmonic Oscillator. But the Hermite Polynomials are real, not complex. I thought that solutions to the Schrödinger equation always had to be complex. What am I not understanding? Thanks in advance.
  2. jcsd
  3. Aug 15, 2010 #2


    User Avatar

    Staff: Mentor

    You're missing the time-dependent phase factor. Energy eigenstates generally look like this, in their time-dependent form:

    [tex]\Psi_n(x,t) = \psi_n(x) e^{-iE_n t / \hbar}[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook