Analytic solution of the relativistic Coulomb problem for a spinless Salpeter equation
We construct an analytic solution to the spinless S-wave Salpeter equation for two quarks interacting via a Coulomb potential, (2(-del/sup 2/+m/sup 2/)/sup 1/2/-M-..cap alpha../r) psi(r) = 0, by transforming the momentum-space form of the equation into a mapping or boundary-value problem for analytic functions. The principal part of the three-dimensional wave function is identical to the solution of a one-dimensional Salpeter equation found by one of us and discussed here. The remainder of the wave function can be constructed by the iterative solution of an inhomogeneous singular integral equation. We show that the exact bound-state eigenvalues for the Coulomb problem are M/sub n/ = 2m/(1+..cap alpha../sup 2//4n/sup 2/)/sup 1/2/, n = 1,2,..., and that the wave function for the static interaction diverges for r..-->..0 as C(mr)/sup -nu/, where ..nu.. = (..cap alpha../..pi..)(1+..cap alpha../..pi..+...) is known exactly.
- Research Organization:
- Physics Department, University of WisconsinMadison, Madison, Wisconsin 53706
- OSTI ID:
- 5828714
- Journal Information:
- Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 28:2; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANALYTICAL SOLUTION
BETHE-SALPETER EQUATION
BOUND STATE
BOUNDARY-VALUE PROBLEMS
COULOMB FIELD
EIGENVALUES
ELECTRIC FIELDS
EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
INTEGRAL EQUATIONS
INTERACTIONS
ITERATIVE METHODS
PARTIAL WAVES
PARTICLE INTERACTIONS
QUARK-QUARK INTERACTIONS
RELATIVITY THEORY
S WAVES
WAVE FUNCTIONS