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

[Tim Sullivan x5830 <sullivan@kenyon.edu>]

David Bowman writes:
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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'. 

<snipped other good stuff>

David Bowman
dbowman@georgetowncollege.edu

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Thank you for the tactful correction, you are absolutely right.

The point being that quantum mechanics saved us from the consequences
of assuming classical motion at the quantum level. If the electron in
the ground state of the hydrogen atom is considered to be in motion in
a classical sense, then it should (among other things) radiate, lose
energy and spiral into the nucleus. This doesn't happen and Bohr with
great insight worked out the consequences postulating the existence of
these non-classical stationary states.

But the flip side of this is that when you want a quantum picture of 
motion (something changing with time) you need to involve more than one
quantum state. You can see this in Bohr's own application of the
correspondence principle. He knows that if the quantum number gets large
enough the his model of the hydrogen atom must approach a classical model.
So he compares the radiation from a classical particle in orbit around the
nucleus to the radiation emitted in a transition between adjacent states
in the large quantum number limit. Another example of this is when you 
want to model a free particle whose position varies with time, you need
to form a wavepacket, i.e., a superposition of states.

So what do I tell the first year student that wants to know how the electron
knows about the existence of the second level? I try to explain that to disturb
or shake the hydrogen atom in its ground state necessarily involves another
state, because that is the flip side of the invention of stationary states.
And, as mentioned in the previous post, I talk about resonance ideas.

Tim Sullivan
sullivan@kenyon.edu