Abstract
The adiabatic hypothesis of old quantum theory which formed the basis for Bohr-Sommerfeld quantization assumed that the adiabatic invariants of multiply periodic mechanical systems should be quantized with the discrete values or sometimes , where is Planck's constant. The hypothesis did not follow from any more general assumption. In the present paper we derive some related results within the theory of classical electrodynamics with classical electromagnetic zero-point radiation. We derive the fact that the adiabatic invariants of a charged nonrelativistic periodic mechanical system with no harmonics remain adiabatic invariants when placed in the classical electromagnetic zero-point radiation spectrum and only in this spectrum. Furthermore the phase-space distribution for the three-dimensional mechanical system in zero-point radiation becomes leading to the average value for each of the adiabatic invariants. Here , which is naturally chosen as Planck's constant, is just the scale factor appearing in the classical zero-point radiation. For each of the systems in equilibrium with zero-point radiation already treated in the literature, we sketch the connection with the unifying formalism of action-angle variables.
- Received 5 October 1977
DOI:https://doi.org/10.1103/PhysRevA.18.1238
©1978 American Physical Society