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Harmonic Oscillator-Normalisation & Annihilation Operator

  1. Apr 6, 2007 #1
    The problem statement, all variables and given/known data

    [tex] \psi(x) = N\sum_{n=0}^\infty \frac{\beta^n}{\sqrt{n!}}\psi_n(x) [/tex]
    And [tex] \psi_n(x) [/tex] has eigenvalue [tex] E_n = (n + 1/2)\hbar\omega [/tex].

    - Determine N (normalisation constant).
    - Show [tex] \psi(x) [/tex] is an eigenstate of 'a' (annihilation operator).

    The attempt at a solution

    I don't know how to normalise it because [tex] \psi_n(x) \propto (a^+)^n \psi_0(x) [/tex] which makes things unusually complicated.

    As for showing the eigenstate do I just operate 'a' on [tex] \psi(x) [/tex], expand, and get it in terms of [tex] \psi(x) [/tex] again?

    (By the way how do I preview this post to check my tex? It keeps saying "Reload this page in a moment")
  2. jcsd
  3. Apr 7, 2007 #2
    no worries.

    All done :)
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