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Given what we discussed in class today (Mon), focus on questions which may arise from sections 2 to 4. Yuichi.

Page 65 Griffiths shows how to calculate the group velocity for wave function made up of many frequencies. It seems to me that the shape of the wave would change (different freq. would travel at different velocities) if the higher order derivatives of the frequency were non zero, am I interpreting this correctly?

One issue concerning quantum mechanics has always bothered me. Why was is a wave model assumed for quantum events? Is this solely in attempt to match experimental observation? Wave mechanics is still classical in foundation quantum happenings seem to be in a completely scheme than classical events, which is the source of my discontent. Have other models been successfully applied to quantum mechanics?

It is my understanding that the wave model was derived and created before very much experimental observation had been made at all (at least on small scales… we've still not got very good small scale observational skills, instruments limited as they are) . But I believe this is born in part from Planck's discovery of light quanta and Einstein's wave-particle duality description of light. As well as an attempt at explaining the behavior of electrons staying in orbital – so inherently there was a need for quantized energy levels.

But I agree with you. It seems as if it is in a lot of ways simply a mathematical tool to describe what we are limited in experiencing because of our physical distance from the extreme spatial spaces. I've often wondered how quantum mechanics would be if we could somehow shrink ourselves to sizes of molecules and atoms. Would we still be describing atoms as probabilities – or if we were smaller and we didn't have to contribute so much to the uncertainty principle in observing these things. If an amoeba could study quantum mechanics, would he agree with us? Basically … is our knowledge of QM and the wave 'true' or is it just a model to explain what we can't physically know…

I think you should come up with a new model. Something Einstein would like better!

I don't quite understand how Griffith went from equation [2.2] to equation [2.3]. Can someone add some mathematical commentary to the separation of variables steps?

What exactly is a stationary state? They talk a little bit about it on page 26 of Griffiths…Is it just every solution of the time independent solution to the Sch. Eqn.?