Quantum mechanical derivation of ohm's law?

[johnathon]

I'm watching MIT 8.02 electricity and magnetism () and the lecturer says that there is a derivation of ohm's law but it uses quantum mechanics which is outside the scope of the course. Does anybody know of this derivation and can point me to it? I searched around but can't find anything

 

[kith]

The linear relationship I~V (respectively j~E) can be derived from the classical Drude theory. This is what's usually called Ohm's Law.

What is not predicted correctly is the proportionality factor R (respectively ρ). See maybe http://en.wikipedia.org/wiki/Classical_and_quantum_conductivity.

 

[physwizard]

I'm watching MIT 8.02 electricity and magnetism () and the lecturer says that there is a derivation of ohm's law but it uses quantum mechanics which is outside the scope of the course. Does anybody know of this derivation and can point me to it? I searched around but can't find anything

the basic model for conduction is the drude model. this assumes that electrons behave like billiard balls. this is enough to prove ohms law. the quantum model is the drude-sommerfield model. here electrons behave like waves and scatter off impurity atoms. then there is a more advanced model call nearly free electron model. anyways the quantum theory successfully explains the temperature dependence of resistivity which the classical drude model is not able to . i would say not to bother with derivations, the important thing is to understand how conduction happens from the quantum mechanical perspective.

 

[johnathon]

the basic model for conduction is the drude model. this assumes that electrons behave like billiard balls. this is enough to prove ohms law. the quantum model is the drude-sommerfield model. here electrons behave like waves and scatter off impurity atoms. then there is a more advanced model call nearly free electron model. anyways the quantum theory successfully explains the temperature dependence of resistivity which the classical drude model is not able to . i would say not to bother with derivations, the important thing is to understand how conduction happens from the quantum mechanical perspective.

So can ohm's law be derived from the nearly free electron model?

 

[StevieTNZ]

Interesting article on Ohm's law in the quantum scale - http://physicsworld.com/cws/article/news/48242