Spinless Salpeter Equation: Laguerre Bounds on Energy Levels

Abstract

The spinless Salpeter equation may be considered either as a standard approximation to the Bethe--Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the costumary nonrelativistic Schrödinger formalism. Because of the presence of the rather difficult-to-handle square-root operator of the relativistic kinetic energy in the corresponding Hamiltonian, very frequently the corresponding (discrete) spectrum of energy eigenvalues cannot be determined analytically. Therefore, we show how to calculate, by some clever choice of basis vectors in the Hilbert space of solutions, for the rather large class of power-law potentials, at least (sometimes excellent!) upper bounds on these energy eigenvalues, for the lowest-lying levels this even analytically.

arXiv comment16 pages, LaTeX

References in corpus (6)

• Relativistic Coulomb Problem: Analytic Upper Bounds on Energy Levels
• A Variational Approach to the Spinless Relativistic Coulomb Problem
• Semi-Relativistic Hamiltonians of Apparently Nonrelativistic Form
• Relativistic Coulomb Problem: Energy Levels at the Critical Coupling Constant Analytically
• All Around the Spinless Salpeter Equation
• Effective Potential Models for Hadrons

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