- #1
intervoxel
- 195
- 1
I'm confused about these two forms of the raising/lowering operators for the harmonic oscillator.
When each one is used?
[tex]
a_+\psi_n=i\sqrt{(n+1)\hbar\omega} \psi_{n+1}
[/tex]
[tex]
a_-\psi_n=-i\sqrt{n\hbar\omega} \psi_{n-1}
[/tex]
[tex]
a_+|\psi_n\rangle=\sqrt{n+1} |\psi_{n+1}\rangle
[/tex]
[tex]
a_-|\psi_n\rangle=\sqrt{n} |\psi_{n-1}\rangle
[/tex]
When each one is used?
[tex]
a_+\psi_n=i\sqrt{(n+1)\hbar\omega} \psi_{n+1}
[/tex]
[tex]
a_-\psi_n=-i\sqrt{n\hbar\omega} \psi_{n-1}
[/tex]
[tex]
a_+|\psi_n\rangle=\sqrt{n+1} |\psi_{n+1}\rangle
[/tex]
[tex]
a_-|\psi_n\rangle=\sqrt{n} |\psi_{n-1}\rangle
[/tex]
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