Visual Quantum Mechanics

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Shifted eigenstate of the harmonic oscillator

Here we see the second eigenstate, initially shifted to x=-3. For this state the absolute value of the wave function (and hence the position probability density) retains a constant shape during the time evolution. The expectation values of position and momentum perform a classical motion.

"Visual Quantum Mechanics - Book One" describes the motion of arbitrary wave packets in the field of the harmonic oscillator.