Perturbation theory with respect to Planck's constant

Timothy H. Boyer

We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

G. Matteucci, Conradin Beeli

An alternative approach with respect to the standard double-slit experiment is presented to introduce the wave-like behavior of electrons. This simple and pedagogical experiment requires a commercial transmission electron microscope and a ferromagnetic film transparent to electrons. It allows in addition the measurement of Planck’s constant.

Reiner M. Dreizler, Eberhard K. U. Gross

Timothy H. Boyer

One should not confuse a physical constant with a theory which incorporates the constant. Planck's constant h can appear in classical or quantum theories.