n0_3sc
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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")
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")