Energy bounds for the spinless Salpeter equation: harmonic oscillator

Details Energy bounds for the spinless Salpeter equation: harmonic oscillator Energy bounds for the spinless Salpeter equation: harmonic oscillator

2000-12-14

arxiv.org/abs/hep-th/0012127v1

J.Phys.A34:5059-5064,2001

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, 1 figure

Scientific paper

10.1088/0305-4470/34/24/304

We study the eigenvalues E_{n\ell} of the Salpeter Hamiltonian H = \beta\sqrt(m^2 + p^2) + vr^2, v>0, \beta > 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 + \beta\sqrt(m^2 + r^2)} provides both upper and lower energy bounds for all the eigenvalues of the problem.

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