- #1
n0_3sc
- 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")
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")