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Harmonic Oscillator-Normalisation & Annihilation Operator

  • Thread starter n0_3sc
  • Start date
  • #1
243
1
Homework Statement

Wavefunction:
[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")
 

Answers and Replies

  • #2
243
1
no worries.

All done :)
 

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