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Re: a question from an AP Chem student...



Regarding Tim Sullivan's comment:
....
And the lesson of the quantum harmonic oscillator is that to get something corresponding
to classical swinging or sloshing one needs to have a mixture of states. Recall that the
states corresponding to individual levels are called "stationary states" because they are
time independent. So resonance, or the excitation of motion, involves mixtures of states
necessarily. ....

I suspect it was only a slip of the fingers in Tim's choice of words, but
it is not true that a *mixture* of stationary states is time dependent.
Usually, physicists make a technical distinction of meaning between the
term 'mixture' and the term 'superposition'. It is a *superposition* of
multiple stationary states that is dynamic. A mixture (represented by a
density matrix/operator) is an *incoherent* statistically weighted
combination of (projections onto pure) states that exhibits no dynamic
interference between its constituent stationary pure states (assuming for
the moment that its constituent pure states are themselves indeed
stationary). But a *superposition* of states is a *coherent* pure state
linear combination of states represented by a time dependent wave function
which *does* exhibit all sorts of dynamic interference effects between its
constituent (stationary) states where the rates at which the interference
patterns change (i.e. rates of relative phase shift) are equal to the
energy differences between those constituent stationary states divided by
h-bar.

David Bowman
dbowman@georgetowncollege.edu