4 research outputs found
An algebraic SU(1,1) solution for the relativistic hydrogen atom
The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found
taking advantage of the Lie algebra in which the radial part of the
problem can be expressed. For defining the algebra we need to add to the
description an additional angular variable playing essentially the role of a
phase. The operators spanning the algebra are used for defining ladder
operators for the radial eigenfunctions of the relativistic hydrogen atom and
for evaluating its energy spectrum. The status of the Johnson-Lippman operator
in this algebra is also investigated.Comment: to appear in Physics Letters A (2005). We corrected a misprint in
page 7, in the paragraph baggining with "With the value of ..." the ground
state should be |\lambda, \lambda>, not |\lambda, \lambda+1