Yes this is the usual textbook treatment of the Casimir force as given on www.cs.mcgill.ca. The classical Casimir force is given by equation (21), and is proportional to the total relativistic energy E. This is reduced as in Eq. (23), so we are dealing with the Casimir force on an electron in an energy level of the H atom. The macroscopic problem is a different one, and in that context you remarks can be developed. The m(r) function is defined by the infinitesimal line element and the m space. So this note introduces the Casimir force on an electron in the H atom. This is a new idea.

Note 430(3)

If I see it right, eq.(2) is a standing wave in the Casimir volume

between the metallic plates. I would expect that all three terms were

either complex or real valued, but anyway.

When applying classical theroy to the Casimir problem, I would expect

that U_0 is the potential between the two plates. Because of condition

(23) it seems not to play a role, is this correct?

In the final result the Casimir force acting on a particle only depends

on its momentum. How is m(r) defined? From the centre of each particle?

It is difficult to understand that this gives a macroscopic force a la

Casimir. Only in the direct vicinity of the particle a force is present.

There seems to be a step missing from the single particle to a (more or

less macroscopic) ensemble.

Horst

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