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Energy bounds for the spinless Salpeter equation: harmonic oscillator

Richard L. Hall·Wolfgang Lucha·Franz F. Schoeberl
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Abstract

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = β\sqrt(m^2 + p^2) + vr^2, v>0, β> 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula E = min_{r > 0} {v(P/r)^2 + β\sqrt(m^2 + r^2)} provides both upper and lower energy bounds for all the eigenvalues of the problem.

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Richard L. Hall, Wolfgang Lucha, Franz F. Schoeberl. 2000-12-14. Energy bounds for the spinless Salpeter equation: harmonic oscillator. https://doi.org/10.1088/0305-4470%2F34%2F24%2F304

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