Periodicity in the SHO

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If a particle is initially in a state which is an even functions of x (

), not necessarily an eigenstate, how much time will pass before the probability distribution first returns to its initial shape

? How long is this repeat time for initial states which are arbitrary odd functions of x? How long for completely arbitrary initial states?

Prof. Tomas Alberto Arias
Sat Apr 20 19:52:25 EDT 1996