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Matrix representation of the nonlocal kinetic energy operator, the spinless Salpeter equation and the Cornell potential

Journal Article · · Physical Review, D (Particles Fields); (United States)
 [1]
  1. Department of Physics and Astronomy, Bowling Green State University, Bowling Green, Ohio 43403-0224 (United States)
+ Show Author Affiliations
A new procedure for solving the spinless Salpeter equation is developed. This procedure is implemented with the Cornell potential, where all of the required matrix elements can be calculated from analytic expressions in a convenient basis. Beginning with analytic results for the square of the momentum operator, the matrix elements of the nonlocal kinetic energy operator are obtained from an algorithm that computes the square root of the square of the relativistic kinetic energy operator. Results calculated with the spinless Salpeter equation are compared with those obtained from Schroedinger's equation for heavy-quark systems, heavy-light systems, and light-quark systems. In each case the Salpeter energies agree with experiment substantially better than the Schroedinger energies.
OSTI ID:
7233539
Journal Information:
Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 50:1; ISSN PRVDAQ; ISSN 0556-2821
Country of Publication:
United States
Language:
English

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Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
662240 -- Models for Strong Interactions-- (1992-)
662420 -- Properties of Mesons & Meson Resonances-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
BETHE-SALPETER EQUATION
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
ENERGY
EQUATIONS
FERMIONS
KINETIC ENERGY
LINEAR MOMENTUM OPERATORS
MATHEMATICAL LOGIC
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
PARTIAL DIFFERENTIAL EQUATIONS
POSTULATED PARTICLES
POTENTIALS
QUANTUM OPERATORS
QUARKS
SCHROEDINGER EQUATION
WAVE EQUATIONS