How does a quantum harmonic oscillator oscillate?

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closet mathemetician
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A classical harmonic oscillator follows a smooth, sinusoidal path of oscillation. Since on a quantum level energy levels are discrete, does a quantum harmonic oscillator actually oscillate in the everyday sense?
 

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closet mathemetician said:
does a quantum harmonic oscillator actually oscillate in the everyday sense?
No, it doesn't.

In classical physics x=x(t) is moving around. In qm what is moving around with the classical frequency is the qm operator x(t) in the Heisenberg picture.
 

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