Shouldn't a metal at 0K emit electromagnetic radiation?

[voila]

Electrons pile up inside a metal up to a maximum value in k-space (meaning the have velocity) and occupying all levels at 0K, solving the Schroedinger equation as running waves. So electrons moving => radiation being emitted. But electrons can't move to a lower energy state, so that would mean energy being emitted without slowing the electrons down. I must be obviously not getting something.

 

[The_Duck]

Your reasoning correctly shows that a metal (or anything else) at 0K will *not* radiate.

So electrons moving => radiation being emitted.

This is an oversimplification. In quantum mechanics it is not as simple as "moving charges radiate."

It may be simpler to consider an atom, because the situation is exactly the same there. Suppose we have a hydrogen atom in the ground state. The expectation value of the electron's kinetic energy is nonzero, so in some sense the electron is "moving." Nonetheless it cannot radiate because there is no lower energy state for the electron to go to.

 

[M Quack]

This is a common misconception about quantum mechanics in general, and the Hydrogen atom in particular. The angular momentum of the electron was interpreted as a real motion of the electron about the nucleus. The magnetic moment corresponds to a current. This interpretation was shown to be wrong and over-simplified time and again. Angular momentum, wave vectors, etc. do not imply any moving charges, hence there is no radiation emitted in the ground state or other Eigenstates of the Hamiltonian.

 

[voila]

Thought the "real velocity" of the particle (excuse the term) was given by the group velocity of the wavefunction, which happens to be non-zero. So I don't really get when interpret this as a "moving electron" that would emitt radiation and when not, appart from comon sense.

 

[The_Duck]

So I don't really get when interpret this as a "moving electron" that would emitt radiation and when not, appart from comon sense.

In some sense all particles are always "moving," because of the uncertainty principle. So in QM you should not try to use this as a guide to when charged particles will radiate.

A decent rule of thumb is probably: a charged particle will always radiate photons (at some rate) if it can do so while conserving energy and momentum.

 

[voila]

A decent rule of thumb is probably: a charged particle will always radiate photons (at some rate) if it can do so while conserving energy and momentum.

Guess you meant "if it can do so while lowering its energy (having lower energy states available) or if it has a something supplying energy" or something like that. Thanks for the help M Quack and The_Duck

 

[Sonderval]

You may also take into account that you can linearly combine the +k- and -k-waves of the ground state to a standing wave that does not move. (This is the same procedure that gets you the band gap in the weak potential limit.)

 

[Khashishi]

One way to think about it is:
Things that radiate electromagnetic waves will also absorb electromagnetic waves. (Moving electrons can also absorb light.) And they will only have a net radiation if the temperature of the thing is higher than the temperature of the surrounding environment. A metal at 0K (impossible) is colder than the surrounding environment, so it will be absorbing radiation from the environment.