Physical Review A

Relativistically corrected Schrödinger equation

M. Kissel-Phillip, W. H. Eugen Schwarz

Published Dec 1, 1988• 12 citations

Abstract

The relativistically corrected Schr\"odinger (RS) equation [(${m}^{2}$${c}^{4}$+${p}^{2}$${c}^{2}$${)}^{1/2}$ +V-E]\ensuremath{\Psi}=0 is sometimes used to describe charged fermions, which are subject to strong Zitterbewegung. Since, however, equations of this type describe bosons with weak Zitterbewegung effects, it is mandatory to screen the Coulomb potential V in an r range of order h/mc, and also to add a screened spin-orbit potential. Thereby the singularity problems with Coulomb potentials are avoided. While the Pauli Hamiltonian must not be used in variational or eigenvalue equations, the RS Hamiltonian may be. An effective potential for the RS equation is derived, which yields relativistically corrected energies and wave functions for fermion systems with Coulomb potentials. Accurate numerical solutions for an unshielded single-center Coulomb potential are presented.

DOI: 10.1103/physreva.38.6027

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