About the Equations of Electromagnetism and Quantum Mechanics

C. G. DARWIN

Horst E. Wilhelm

A formulation of the quantum mechanics of charged particles in time‐dependent electromagnetic fields is presented, in which both the Schroedinger equation and wave equations for the electromagnetic potentials are Galilei covariant, it is shown that the Galilean relativity principle leads to the introduction of the electromagnetic substratum in which the matter and electromagnetic waves propagate. The electromagnetic substratum effects are quantitatively significant for quantum mechanics in reference frames, in which the substratum velocity w is in magnitude comparable with the velocity of light c. The electromagnetic substratum velocity w occurs explicitly in the wave equations for the electromagnetic potentials but not in the Schroedinger equation.

Jaroslav Zamastil, Jakub Benda

Aubrey Truman, Huaizhong Zhao

In this paper we consider the ℏ→0 asymptotics for the solutions to stochastic Schrödinger equations for quantum mechanical particles in random electromagnetic fields in Rn. We obtain semi-classical expansions for their solutions up to any order in L2(Rn) a.s. by using a stochastic Hamilton Jacobi equation and a stochastic continuity equation. We conclude that as ℏ→0 the stochastic quantum mechanics with random electromagnetic fields tends to stochastic classical mechanics.

Weixing Xu

In this work a new representation of quantum mechanics, that is, the electromagnetic field representation, is proposed, which is different from the Schr dinger`s equation and Heisenberg`s Matrix. It is pointed out that even though the results from Schr dinger`s equation, Heisenberg`s Matrix and electromagnetic field representation in describing the quantum system are the same, the principles and procedures in describing the quantum system are totally different. The further result regarding the application of the electromagnetic field representation of quantum mechanics to different atomic and molecular systems will be presented later.

Charles T. Sebens