Wave Functions for Harmonically Bound Electrons in an Electromagnetic Field

Mikhail Vladimirovich Fedorov

Meng-Yun Lai, Xiao‐Yin Pan, Yuqi Li

Qixue Wu, 漳州师范学院物理系，漳州 363000

Quantum theory of double-wave function description (DWFD) is applied to describe the motion of spinning electron in both perpendicular uniform electromagnetic field and two-dimensional harmonic oscillator potential field.The time evolution equations of related mechanical quantities are derived.Furthermore,DWFD of spin-zero electron in the same fields is also given,and it is found that their classical limit results correspond to those of classical mechanics.

Xie Rang-mian

Quantum theory with doublewave function description(DWFD) is applied to describe the motion of spinning electron in two mutually perpendicular uniform electromagnetic fields as well as in twodimensional harmonic oscillator's potential field.A comparison between the classical limit results and those of classical mechanics is made.

C. JAYARATNAM ELIEZER

Dirac's wave equation of an electron enables one to solve for the wave function of an electron moving in an electromagnetic field. The wave function ψ has 4 components ψ1, ψ2, ψ3, ψ4, and the electromagnetic field is described by a four-vector Aμ, consisting of a scalar potential φ and a vector potential A. In the usual problem, we solve for the wave function ψ when the potential Aμ is given. By doing so, we obtain the wave function of an electron which moves in a given electromagnetic field. It is of some interest to consider the reverse question: given the wave function ψ, what can we say about the electromagnetic potential Aμ, which is connected with ψ by Dirac's equation? Is Aμ uniquely determined, and if not, what is the extent to which it is arbitrary ?