Are Feynman's Equations on Superconductivity Valid?

[Demystifier]

In the last chapter of "Feynman Lectures on Physics" part III, Feynman discusses superconductivity. I am particularly intrigued by his equations (21.19) and (21.31), and even more by (21.38). Is there any experimental evidence for validity of these equations?

The question of validity of these equations is particularly important for foundations of quantum mechanics:
https://www.physicsforums.com/showthread.php?t=448366

 

[DrDu]

Maybe you could write down the formulas for our convenience? Thank you.

 

[Demystifier]

Well, it is important to understand the whole context in which the equations are derived. Therefore, it would be better to read the whole section in the book. The book itself is well known, so I assume that most serious physicists have it.

Let me just say that the equations describe the velocity (describing the electron current in a superconductor) and acceleration of electrons as a function of the wave function and the external electromagnetic field. In particular, the velocity has one term proportional to the electromagnetic potential and another term proportional to the divergence of the phase of the wave function. The acceleration has a classical term and a quantum correction that strongly depends on the wave function.

 

[f95toli]

These equations (as well as the rest of the chapter) are just what I guess you could call "classical" (pre-BCS) supeconductivity, so yes their validity were verified ages ago (21.19 is what you use to derive the Meissner effect).
However, thyey do not give a correct microscopic description of superconductivity, I am too tired to read the whole chapter now; but Feymann is -as far as I remember-mainly just using the two-fluid model.
You can find more information in one of the standard texts about superonductivity (e.g. Tinkham)

 

[Demystifier]

so yes their validity were verified ages ago (21.19 is what you use to derive the Meissner effect).

(21.19) is relatively trivial when the electric field is constant. But is (21.19) tested for the case of a non-constant (either in space or time) field? And what about a test of (21.38)?