Semirelativistic Treatment of Bound States

Abstract

This talk reviews several aspects of the "semirelativistic" description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating relativistic effects) and, in particular, presents or recalls some very simple and elementary methods which allow to derive rigorous statements on the corresponding solutions, that is, on energy levels as well as wave functions. In principle, these methods work for all physical situations which may be formulated as an eigenvalue problem.

LaTeX, 18 pages; invited talk by W. Lucha at the Symposium on "Quarks in Hadrons and Nuclei" (202. WE-Heraeus Seminar), September 14 - 19, 1998, Rothenfels Castle, Oberwoelz, Austria

Cited by in corpus (45)

• The Rest-Frame Darwin Potential from the Lienard-Wiechert Solution in the Radiation Gauge
• Relativistic Harmonic Oscillator
• Energy bounds for the spinless Salpeter equation: harmonic oscillator
• Discrete Spectra of Semirelativistic Hamiltonians
• Discrete spectra of semirelativistic Hamiltonians from envelope theory
• Quality of Variational Trial States
• Higher order Schrodinger and Hartree-Fock equations
• Energy bounds for the spinless Salpeter equation
• Instantaneous Bethe-Salpeter equation: improved analytical solution
• Analytic Bethe-Salpeter Description of the Lightest Pseudoscalar Mesons
• The Spinless Relativistic Woods-Saxon Problem
• Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
• Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation
• Instantaneous Bethe-Salpeter Equation: Analytic Approach for Nonvanishing Masses of the Bound-State Constituents
• Constructing the $J^{P(C)}=1^{-(+)}$ light flavor hybrid nonet with the newly observed ${\eta }_1(1855)$
• Klein-Gordon lower bound to the semirelativistic ground-state energy
• Instantaneous Bethe-Salpeter Kernel for the Lightest Pseudoscalar Mesons
• Upper limit on the number of bound states of the spinless Salpeter equation
• Relativistic N-Boson Systems Bound by Oscillator Pair Potentials
• Instantaneous Bethe-Salpeter equation: utmost analytic approach
• Accuracy of Approximate Eigenstates
• Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction
• Schroedinger models for solutions of the Bethe-Salpeter equation in Minkowski space
• A semirelativistic treatment of spinless particles subject to the Yukawa potential with arbitrary angular momenta
• The One-Dimensional Spinless Relativistic Coulomb Problem
• The Spinless Relativistic Hulthén Problem
• Gravitating semirelativistic N-boson systems
• The Spinless Relativistic Yukawa Problem
• A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential
• Binding energies of semirelativistic N-boson systems
• Semirelativistic Bound-State Equations: Trivial Considerations
• Electric Polarizability of Mesons in Semirelativistic Quark Models
• Analytical Solution of two-body spinless Salpeter Equation for Hellmann Potential
• The Spinless Relativistic Kink-Like Problem
• The Spinless Relativistic Hellmann Problem
• Schrödinger Models for Solutions of the Bethe-Salpeter Equation in Minkowski Space. II. Fermionic Bound-State Constituents
• Relative variables of the exact fermion-antifermion bound state wave-function in the Schwinger Model
• Goldstonic pseudoscalar mesons in Bethe-Salpeter-inspired setting
• The Semi-Relativistic Equation Via the Shifted-l Expansion Technique
• Numerical Solution of the Spinless Salpeter Equation by a Semianalytical Matrix Method (a Mathematica 4.0 routine)
• Relative energy dependence of the Bethe-Salpeter amplitude in two-dimensional massless QED
• Tunneling dynamics of the relativistic Schrodinger/Salpeter equation
• Simplified Bethe-Salpeter Description of Basic Pseudoscalar-Meson Features
• Semirelativistic Potential Modelling of Bound States: Advocating Due Rigour
• Bethe-Salpeter Bound-State Solutions: Examining Semirelativistic Approaches