Energy bounds for the spinless Salpeter equation: harmonic oscillator

Hall, Richard L.; Lucha, Wolfgang; Schoeberl, Franz F.

Energy bounds for the spinless Salpeter equation: harmonic oscillator

Authors

Hall, Richard L.

Lucha, Wolfgang

Schoeberl, Franz F.

Description

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.
8 pages, 1 figure