Spinless Salpeter Equation: Laguerre Bounds on Energy Levels

Details Spinless Salpeter Equation: Laguerre Bounds on Energy Levels Spinless Salpeter Equation: Laguerre Bounds on Energy Levels

1996-09-11

arxiv.org/abs/hep-ph/9609322v1

Phys.Rev.A56:139-145,1997

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, LaTeX

Scientific paper

10.1103/PhysRevA.56.139

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 Schr\"odinger 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.

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