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

Journal Article · Fri Jul 01 00:00:00 EDT 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.447· OSTI ID:7233539

Fulcher, L P ^[1]

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1. Department of Physics and Astronomy, Bowling Green State University, Bowling Green, Ohio 43403-0224 (United States)

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), Vol. 50:1; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

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