A Salpeter Equation in Position Space: Numerical Solution for Arbitrary Confining Potentials
Feb, 1984
36 pages
Published in:
- Phys.Rev.D 30 (1984) 660,
- Phys.Rev.D 30 (1984) 1995 (erratum)
DOI:
Report number:
- MAD/TH-153
Citations per year
Abstract: (APS)
We present and test two new methods for the numerical solution of the relativistic wave equation [(−∇2+m12)12+(−∇2+m22)12+V(r)−M]ψ(r→)=0, which appears in the theory of relativistic quark-antiquark bound states. Our methods work directly in position space, and hence have the desirable features that we can vary the potential V(r) locality in fitting the qq¯ mass spectrum, and can easily build in the expected behavior of V for r→0,∞. Our first method converts the nonlocal square-root operators to mildly singular integral operators involving hyperbolic Bessel functions. The resulting integral equation can be solved numerically by matrix techniques. Our second method approximates the square-root operators directly by finite matrices. Both methods converge rapidly with increasing matrix size (the square-root matrix method more rapidly) and can be used in fast-fitting routines. We present some tests for oscillator and Coulomb interactions, and for the realistic Coulomb-plus-linear potential used in qq¯ phenomenology.- BOUND STATE: (QUARK ANTIQUARK)
- RELATIVISTIC
- BETHE-SALPETER EQUATION
- QUARK: CONFINEMENT
- POTENTIAL: CONFINEMENT
- MODEL: OSCILLATOR
- POTENTIAL: COULOMB
- MATHEMATICAL METHODS
- NUMERICAL CALCULATIONS
References(26)
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