## Solutions of the relativistic two-body problem II quantum mechanics

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##### Date

1972-08

##### Authors

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##### Journal ISSN

##### Volume Title

##### Publisher

Australian Atomic Energy Commission

##### Abstract

This second paper of a series discusses the formulation of the quantum mechanical equivalent of the relative time classical theory put forward in Part 1. The relativistic wave function is derived and a covariant addition theorem put forward which allows a covariant scattering theory to be established. The free particle eigenfunctions are not plane waves and a covariant partial wave analysis is given. A means is given by which wave functions which yield probability densities in 4-space can be converted to ones yielding the equivalent 3-space density. Bound states are considered and covariant analogues are given of the harmonic oscillator potential, Coulomb potential, the square well potential, and two-body fermion interactions. RESEARCH ARTICLE Previous Next Contents Vol 25 (2)
Solutions of the Relativistic Two-Body Problem. II. Quantum Mechanics
JL Cook
Australian Journal of Physics 25(2) 141 - 166
Published: 1972
Abstract
This paper discusses the formulation of a quantum mechanical equivalent of the relative time classical theory proposed in Part I. The relativistic wavefunction is derived and a covariant addition theorem is put forward which allows a covariant scattering theory to be established. The free particle eigenfunctions that are given are found not to be plane waves. A covariant partial wave analysis is also given. A means is described of converting wavefunctions that yield probability densities in 4-space to ones that yield the 3-space equivalents. Bound states are considered and covariant analogues of the Coulomb potential, harmonic oscillator potential, inverse cube law of force, square well potential, and two-body fermion interactions are discussed.

##### Description

##### Keywords

Quantum mechanics, Relativity theory, Scattering, Angular momentum, Bosons, Harmonic potential

##### Citation

Cook, J. L. (1972). Solutions of the relativistic two-body problem II quantum mechanics. (AAEC-TM-602). Lucas Heights, NSW: Australian Atomic Energy Commission.