A question from a beginner:(adsbygoogle = window.adsbygoogle || []).push({});

If the position operator changes a state vector into a wave function, how does one change a wave function back into a state vector? I have read that the position operator for a one-dimensional vector is simply multiplying by x. Does this mean that what amounts to the inverse position operator (or position inverse operator, perhaps) is putting a

[tex] \frac {1}{x} [/tex]

in front of the wave function? For example, a particle in a one-dimensional "box" of length L has a wave function

[tex]

\psi _n = \sqrt { \frac {2}{L} } sin ( \frac {n \pi x } {L })

[/tex]

Is the corresponding ket

[tex]

| \psi _n \rangle = \frac {1}{x} \sqrt { \frac {2}{L} } sin ( \frac {n \pi x } {L })

[/tex]

This seems logical but something tells me that it is too easy to be correct.

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# From wave to ket

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