Discrete Spectra of Semirelativistic Hamiltonians

Details Discrete Spectra of Semirelativistic Hamiltonians Discrete Spectra of Semirelativistic Hamiltonians

2002-10-16

arxiv.org/abs/hep-th/0210149v1

Int.J.Mod.Phys. A18 (2003) 2657-2680

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 3 figures

Scientific paper

10.1142/S0217751X0301406X

We review various attempts to localize the discrete spectra of semirelativistic Hamiltonians of the form H = \beta \sqrt{m^2 + p^2} + V(r) (w.l.o.g. in three spatial dimensions) as entering, for instance, in the spinless Salpeter equation. Every Hamiltonian in this class of operators consists of the relativistic kinetic energy \beta \sqrt{m^2 + p^2} (where \beta > 0 allows for the possibility of more than one particles of mass m) and a spherically symmetric attractive potential V(r), r = |x|. In general, accurate eigenvalues of a nonlocal Hamiltonian operator can only be found by the use of a numerical approximation procedure. Our main emphasis, however, is on the derivation of rigorous semi-analytical expressions for both upper and lower bounds to the energy levels of such operators. We compare the bounds obtained within different approaches and present relationships existing between the bounds.

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