Radiation in classical and quantum mechanics

[hokhani]

In classical electrodynamics, acceleration of charge generates radiation. In quantum mechanics, radiation is generated by transition of charge from higher quantum lever to lower. Is any relationship between the inter-level transition and acceleration?
Also, how about the radiation of a charge accelerated in a uniform electric field, which there are not stationary states. How to obtain frequency of the radiated light?

 

[Dale]

Is any relationship between the inter-level transition and acceleration?

Both cases have a time-varying dipole moment.

 

[tech99]

I suppose in a simple way that if we accelerate a charge using an alternating electric field, the radiated energy will, as always, be in quanta and the energy of each of these quanta will depend on the frequency of the alternating field.

 

[hokhani]

I suppose in a simple way that if we accelerate a charge using an alternating electric field, the radiated energy will, as always, be in quanta and the energy of each of these quanta will depend on the frequency of the alternating field.

As far as I know, in QM an alternating electric field sets Floquet levels with energy spacing $\hbar \omega$. But I don't know what would happen for electron.

 

[hokhani]

Both cases have a time-varying dipole moment.

From classical view, even in a stationary state of an atom electrons have acceleration and they must radiate.

 

[Dale]

From classical view, even in a stationary state of an atom electrons have acceleration and they must radiate.

Which is why the classical view is wrong.

 

[hokhani]

Which is why the classical view is wrong.

Ok, but do you mean that charge acceleration doesn't generate radiation? Then, what is the classical reason of radiation?

 

[Dale]

Then, what is the classical reason of radiation?

I already answered this: a changing dipole moment.

Ok, but do you mean that charge acceleration doesn't generate radiation?

Whenever charge acceleration produces a changing dipole moment then it generates radiation.

 

[PeterDonis]

what is the classical reason of radiation?

There is no "classical reason" vs. "quantum reason". You are confusing models with reality. Reality is just radiation. The classical model has a more limited domain of validity for making correct predictions about radiation than the quantum model, but both of them are models, not reality.

 

[Dale]

There is no "classical reason" vs. "quantum reason". You are confusing models with reality. Reality is just radiation.

In the classical model there is radiation. And in the quantum model there is also radiation. So there is a classical reason and a quantum reason for radiation, ie the reason that radiation happens in each of the models.