Inhomogeneous Schroedinger equation and its solutions in scattering theory
Journal Article
·
· J. Math. Phys. (N.Y.); (United States)
We prove that psi/sub s/,l, the partial-wave projection of the irregular Coulomb wavefunction psi/sub s/, is a solution of an inhomogeneous Schroedinger equation. New expressions for psi/sub s/,l and psi/sub s/ are obtained in terms of the Coulomb Green functions G/sub C/,l and G/sub C/, respectively. We discuss irregular solutions, the analogs of psi/sub s/, for Coulomb-like and short-range potentials. We find that in general these functions do not approach asymptotically the scattering amplitude times an outgoing spherical wave, in contrast to the pure Coulomb function psi/sub s/.
- Research Organization:
- Natuurkundig Laboratorium der Vrije Universiteit, Amsterdam, The Netherlands
- OSTI ID:
- 6459274
- Journal Information:
- J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 20:5; ISSN JMAPA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
645500* -- High Energy Physics-- Scattering Theory-- (-1987)
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ASYMPTOTIC SOLUTIONS
COULOMB FIELD
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
GREEN FUNCTION
MATHEMATICAL OPERATORS
PARTIAL WAVES
PROJECTION OPERATORS
SCATTERING
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE FUNCTIONS
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ASYMPTOTIC SOLUTIONS
COULOMB FIELD
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
GREEN FUNCTION
MATHEMATICAL OPERATORS
PARTIAL WAVES
PROJECTION OPERATORS
SCATTERING
SCATTERING AMPLITUDES
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE FUNCTIONS