Energy bounds for the spinless Salpeter equation

Details Energy bounds for the spinless Salpeter equation Energy bounds for the spinless Salpeter equation

2001-01-31

arxiv.org/abs/hep-th/0101223v2

J.Math.Phys. 42 (2001) 5228-5237

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, 1 figure

Scientific paper

We study the spectrum of the spinless-Salpeter Hamiltonian H = \beta \sqrt{m^2 + p^2} + V(r), where V(r) is an attractive central potential in three dimensions. If V(r) is a convex transformation of the Coulomb potential -1/r and a concave transformation of the harmonic-oscillator potential r^2, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form E = min_{r>0} [ \beta \sqrt{m^2 + P^2/r^2} + V(r) ] for suitable values of P here provided. At the critical point the relative growth to the Coulomb potential h(r)=-1/r must be bounded by dV/dh < 2\beta/\pi.

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