Ladder Operator (15 min)

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Use the above equation to show that $a^+\vert n\rangle$ is an eigenstate of the number operator $\hat{N}$ . Show that

$\displaystyle a^+\vert n\rangle$

$\displaystyle =$

$\displaystyle \sqrt{n+1}\vert n+1\rangle.$

(41)

(The $\vert n\rangle$ are normalized).

Tobias Brandes 2004-02-04