Hi everyone, Here is a problem I have been wondering about since I was in school. I've never found any answer so I hope someone here might help me. I learned some rules such as resistance in series is R1 + R2 and in parallel it's 1/(1/R1 + 1/R2). Of course there are equations for all sorts of other components connected into a circuit and various other quantities than resistance, for example voltage, amperes, etc. Of course these formula were originally found by experiments and tests, but now quantum physics has got into the understanding of what is actually inside a circuit: electrons through a crystal of metal atoms. What I want to know is how to derive all the laws of circuitry from scratch using this atomic viewpoint. So I hope someone will find this interesting and maybe knows about it!
My suggestion is to read up on transistor theory, it would take to long for us to retype that which is already written.
Can it be done? Probably. But I doubt that anyone on here would know how. I would start with finding some information on the behavior of electrons in different lattice structures under different conditions.
I don't think you are asking about quantum physics. Quantum physics describes the "orbits" of electrons by complex mathematical functions having solutions that correctly describe the energy as in the wavelengths of light absorbed and emitted by excited atoms. The term "quantum" is used because the solutions to the equations involve integral units (quanta) of energy, which are seen as the separation of specific lines of color in the spectrum of light emitted and absorbed by particular atoms as they absorb and emit energy. But for many purposes, thinking of electrons as little objects does seem to work. To get at an answer to your question, look up the "Drude model" http://en.wikipedia.org/wiki/Drude_model This gets at just about what you are asking - using classical mechanics to describe electrical conduction. I don't know much about Drude's paper, but it looks like it would be a good approach to learn more about what you asked.
I think you are asking the wrong questions. Most of the formulas in electronics are derived from Ohm's Law, simple superposition analysis and mathematics, not from quantum theory. Quantum theory does not explain Ohm's Law. Quantum theory deals with the microscopic level. Electricity and electronics work at the macroscopic level. For example, we know how superconductors behave but we still don't know how why they behave the way they do.
As already said, using QM to describe such things as the laws governing electronics might be possible, but the effort would probably not be worth any additional gain that might be had from doing so. However, there are several devices in relatively common use in electronics who's operation can only be described using some of the theories that gave rise to QM. One such device is the tunnel diode. There are others also. Sometimes, though, its just better to go with empirical data to forge ahead. It would be difficult to describe a metal film polyester capacitor or a wire wound resistor in terms of QM. Then again, a tantalum capacitor might well benefit from a study in QM of the factors that allow them to work as they do. As Bill M. suggests, it might serve you well to study some exiting information on this subject.