Schroedinger-like equation for relativistic particles

Journal Article · Mon Jun 01 04:00:00 EDT 1987 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.527537· OSTI ID:6900383

Goldberg, I B; Pratt, R H

The Dirac equation in a spherically symmetric screened Coulomb potential is transformed to a modified Schroedinger equation of the form d/sup 2/u/dr/sup 2/+k/sup 2/(r)u = 0. This transformation is induced by expressing the Dirac function as a linear combination of the function u and its derivative du/dr. Various properties of the transformation and of the resulting equations are studied. The close similarity between the modified Schroedinger equation and the Schroedinger equation suggests that methods applied to the Schroedinger equation to derive nonrelativistic relations can be applied to the modified Schroedinger equation to derive the analogous relativistic relations. As an example, this approach is applied to the single channel quantum defect theory to give a new derivation of its relativistic form.

• Research Organization: Racah Institute of Physics, Hebrew University, Jerusalem, 91904 Israel
• OSTI ID: 6900383
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 28:6; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
CHARGED PARTICLES
COULOMB FIELD
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELASTIC SCATTERING
ELECTRIC FIELDS
ENERGY RANGE
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FUNCTIONAL ANALYSIS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIAL SCATTERING
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SCATTERING
SCHROEDINGER EQUATION
SYMMETRY
TRANSFORMATIONS
WAVE EQUATIONS