Question

How does a complex wavefunction “hold” energy?

Answer 1

Newtonian mechanics is valid only for large objects, whereas quantum mechanics is valid only for very small objects. In Newtonian mechanics the position and velocity of an object can be predicted at a particular time, whereas quantum mechanics can only give probabilities.

Answer 2

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All of the properties of the first wavefunction holdhere too, so this simply describes a particle that is well-localized at that different position.