johnathon said: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
physwizard said: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.
The quantum mechanical explanation of Ohm's law states that the current flowing through a material is directly proportional to the electric field applied and inversely proportional to the resistance of the material. This is due to the movement of charged particles, such as electrons, in a material and their interactions with the electric field.
Classical mechanics explains Ohm's law through the macroscopic behavior of materials, while quantum mechanics delves into the microscopic interactions of particles. In classical mechanics, resistance is viewed as a constant value, while in quantum mechanics, it can vary depending on the energy levels of the material's particles.
Ohm's law can be applied to most materials, but it may not hold true for all materials. In some cases, materials may exhibit non-Ohmic behavior, where the current does not vary linearly with the applied electric field. This is often seen in materials with varying resistance, such as semiconductors.
In quantum mechanics, temperature can affect the resistance of a material by changing the energy levels of its particles. As temperature increases, particles gain more energy and can overcome the resistance in the material more easily, resulting in a decrease in resistance and an increase in current.
The quantum mechanical explanation of Ohm's law is used in various electronic devices and technologies, such as transistors, diodes, and integrated circuits. It also helps in understanding the behavior of materials at the nanoscale, which is crucial in fields like nanotechnology and quantum computing.