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Re: No. I have no argument with Hummel's derivation..Just your methods.

As for SE,,,I've stated before..I only have a 6 month snapshot upon which to evaluate.

For electrons...Kittel seems to provide a better insight into the model..

He points out that QM prevents continuous velocities of electrons. More along the lines of descrete bumps of velocity. It is visible in his diagram of electron momentum, with the fermi sphere as the boundary. The field gradient causes a shift of the sphere, that shift occuring at drift speeds. And within that sphere, the electrons moving from the excluded region left behind the sphere, and "popping" into the newly occupied region on the leading edge. As the sphere is defined as the probability of occupation of momentum states, one can make the "assumption" which Hummel may have, that the transport of the electron from excluded to included regions occurs at thermal speeds. I've five books here now, and all do not make that assumption.

The stretch from transport of electron occupation states at the leading from the trailing edge ocurring thermally, to very few actual electrons doing all the movement, is a stretch that the other five authors are not comfortable making. Perhaps it is the conservation of charge issues which will occur at a boundary that prevented them from doing so.

In reviewing your Hummel quote: it appears to gel quite well with Kittel's model if the word "drift" is removed from Hummel's quote, as it confuses overall drift with the quick QM based jump within the fermi sphere of Kittel. Without that word, the models are the same..

But it is worded in a confusing manner, in a way that basically negates the entire free electron model while at the same time giving the impression that few electrons transport all the current by moving very fast, which was not his intent. He was merely adding some QM to the flavor, unfortunately his choice of words didn't help.

I don't champion either model...I use the appropriate tool for the job. If the drift velocity approaches the thermal, then QM must be used..But that is at gradients that flash the conductor. For normal non cryogenic applications, QM is not needed.

Cheers, John


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