A Note on the Density of Eigenfunctions for an Electron Obeying Dirac's Equation

Kunio Miyoshi, Masayoshi Suzaki

S Gupta

Wataru Ichinose

Hans Albrecht Bethe

M. H. Johnson, Bernard A. Lippmann

The motion of a charged particle in a constant magnetic field is treated in both relativistic and non-relativistic quantum theory. Operators representing the center of the orbit, which obey the commutation law for conjugate variables, are introduced and their connections with energy, angular momentum, and magnetic moment studied. Energy eigenfunctions in an operator form are obtained by factorization. Previously derived eigenfunctions in coordinate space are obtained and are shown to be eigenfunctions for the operators for the center of the orbit as well as for the energy. Corresponding relativistic eigenfunctions are derived by a simple device which enables one to construct solutions of the Dirac equation from solutions of the Schr\"odinger equation.

W Gough

A simple diagram is presented for use with the analysis of the Dirac equation for an atom with a single electron. The complicated expression for the energy of the electron takes on a very simple form. The usual theory is presented with an angle from the diagram as the energy parameter, and the radial parts of the energy eigenfunctions for n = 1 and 2 are calculated.