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Energy bounds for the spinless Salpeter equation

Richard L. Hall·Wolfgang Lucha·F. F. Schoberl
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Abstract

We study the spectrum of the spinless-Salpeter Hamiltonian H = β\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} [ β\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 < 2β/π.

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Richard L. Hall, Wolfgang Lucha, F. F. Schoberl. 2001-10-24. Energy bounds for the spinless Salpeter equation. https://doi.org/10.1063/1.1405848

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