Phase-integral solution of the radial Dirac equation
- Dalarna University, S-78188 Borlaenge (Sweden)
A phase-integral (WKB) solution of the radial Dirac equation is constructed, retaining perfect symmetry between the two components of the wave function and introducing no singularities except at the classical transition points. The potential is allowed to be the time component of a four-vector, a Lorentz scalar, a pseudoscalar, or any combination of these. The key point in the construction is the transformation from two coupled first-order equations constituting the radial Dirac equation to a single second-order Schroedinger-type equation. This transformation can be carried out in infinitely many ways, giving rise to different second-order equations but with the same spectrum. A unique transformation is found that produces a particularly simple second-order equation and correspondingly simple and well-behaved phase-integral solutions. The resulting phase-integral formulas are applied to unbound and bound states of the Coulomb potential. For bound states, the exact energy levels are reproduced.
- OSTI ID:
- 21335929
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 3; Other Information: DOI: 10.1063/1.3328454; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
Similar Records
A detailed study of nonperturbative solutions of two-body Dirac equations
SPECTRAL THEORY OF DIRAC'S RADIAL RELATIVISTIC WAVE EQUATION