ANOMALOUS SOLUTIONS TO THE DIRAC AND SCHRODINGER EQUATIONS FOR THE COULOMB POTENTIAL

Journal Article · Sat Jun 15 04:00:00 EDT 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.130.2506· OSTI ID:4703095

Armstrong, B H

Certain anomalous soiutions to the Dirac and relativistic Schrodinger equations for the Coulomb potential, some of which were not investigated before, are analyzed. These are solutions for orbital angular momentum l = 0 and l = 1/2 in the Schrodinger case and total angular momentum j = 0 in the Dirac case that are quadratically integrable for all energies E < 0. The purpose is to determine if there exist fundamental reasons for discarding them, or if they describe meaningful physical systems. Reasons are given why they may be discarded for real two-body systems, such as the hydrogen atom. These solutions can only be meaningful for systems that have an exact one-body, pure Coulomb relativistic hamiltonian. They are valid for repulsive as well as attractive potentials. It is suggested that the l = 0 relativistic Schrodinger solution be identical as the wave function of a nonrigid charged spherical shell. In addition, it is suggested that a particle fluctuating about its own center of mass in zitterbewegung-type motion may experience a repulsive Coulomb self-potential and have an exact one-particle-type hamiltonian. The charge distributions obtained in this interpretation for two of the solutions have mean radii ontrol migra- e/sup 2//m/sub 0/c/sup 2/ and rms radii ontrol migra- h/m/sub 0/c. (auth

• Research Organization: Lockheed Missiles and Space Co., Palo Alto, Calif.
• NSA Number: NSA-17-026579
• OSTI ID: 4703095
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 130; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ANGULAR MOMENTUM
DIFFERENTIAL EQUATIONS
DIRAC EQUATIONS
DISTRIBUTION
ELECTRIC CHARGES
ELECTRIC POTENTIAL
ELEMENTARY PARTICLES
HAMILTONIAN
MANY BODY PROBLEM
MOMENTUM
MOTION
NUCLEAR MODELS
ORBITS
OSCILLATIONS
PHYSICS
QUANTUM MECHANICS
RELATIVITY THEORY
SCHROEDINGER EQUATION