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Quantum SHO Wave Functions not Complex?

  1. Aug 15, 2010 #1


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    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


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    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]
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