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## Main Question or Discussion Point

Is there a simple expression for the ladder operators, in terms of x and [itex]-i\hbar\partial_x[/itex], for the infinite potential well? After some attempts, I couldn't figure out any nice operators that would map functions like this

[tex]

\sin\frac{\pi n x}{L} \mapsto \sin\frac{\pi(n\pm 1)x}{L}.

[/tex]

[tex]

\sin\frac{\pi n x}{L} \mapsto \sin\frac{\pi(n\pm 1)x}{L}.

[/tex]