Regarding applicability of Maxwell's equations on microscopic structures.

[otaKu]

So from what I seem to understand up until now, Maxwell's equations usually work while assuming that the fields are continuous and smooth instead of the actual complexity at the atomic scale. However, as we move more and more towards the microscopic realm, a point comes when we cannot ignore this miniscule field variations and we need to change our approach. What exactly is that length scale? Is there a specific term for it? What changes do we need to apply to the macroscopic equations to make them work at this regime? I apologise if some of the questions in the thread don't make any sense, I'm rather new to Electrodynamics, especially at the microscopic level and I was wondering about the length scale where things will get troublesome. Thanks.

 

[f95toli]

There is no specific length scale for this. The ME always work, even for extremely small objects.
That said, the ME are -sort of- classical equations and there is e.g. no concept of a photon. Hence, to describe quantum effects you need a formalism known as quantum electrodynamics (QED) which is what you would e.g. use in quantum optics.
However, QED effects can -and frequently are- seen in macroscopic objects. A good example would the microwave resonators used in cavity-QED experiments which are many centimeters in size.
What determines whether you see quantum effects in an experiment is not the physical size of the objects, it is rather the energy scales (and temperatures) involved; typically you need very well engineered environments.

 

[otaKu]

There is no specific length scale for this. The ME always work, even for extremely small objects.
That said, the ME are -sort of- classical equations and there is e.g. no concept of a photon. Hence, to describe quantum effects you need a formalism known as quantum electrodynamics (QED) which is what you would e.g. use in quantum optics.
However, QED effects can -and frequently are- seen in macroscopic objects. A good example would the microwave resonators used in cavity-QED experiments which are many centimeters in size.
What determines whether you see quantum effects in an experiment is not the physical size of the objects, it is rather the energy scales (and temperatures) involved; typically you need very well engineered environments.

So is it safe for me to assume that I probably won't have to deal with quantum electrodynamics if I am dealing with conventional electronic devices such as LEDs and HEMTs?