Motion in an Electromagnetic Field

Earle H. Kennard

A. P. Botin, A. P. Kazantsev, Vladimir S. Smirnov

Nobuo Nagai, Hirofumi Sanada, Takashi Yahagi

The electromagnetic waves derived from the Maxwell equations are characterized by being lossless. It is known that such lossless electromagnetic waves are obtained in the electromagnetic fields of coaxial cables and the electromagnetic fields generated using coils and capacitors. Because the physical behavior and effects of electromagnetic waves differ depending on frequency, the electromagnetic waves propagating through the electromagnetic fields of coaxial cables and the electromagnetic fields generated using coils and capacitors are limited to very high frequency (VHF) and ultrahigh frequency (UHF). Electromagnetic waves of other frequencies are left as problems for future research. Also, as stated in Section 8 of this article, a "lossless circuit" is also derived from the equations of motion for molecules (Newtonian mechanics). Namely, because the oscillations of a periodic system consisting of N molecules are expressed in the representation equivalent to the circuit representation of lossless electromagnetic waves, it has been demonstrated that a lossless circuit also arises from the motion of molecules with mass derived from Newtonian mechanics. This is the key physical phenomenon that links quantum mechanics to mathematics. We will leave this point as an important problem for future research.

Zhan-Wu Bai

The motion of a charged particle passing through semi-infinity uniform electromagnetic field is descriped by double wave quantum theory.To one order WKB approximation,the results are similar to classical mechanics.

L.D. LANDAU, E.M. LIFSHITZ