Lower bounds for the spinless Salpeter equation

Details Lower bounds for the spinless Salpeter equation Lower bounds for the spinless Salpeter equation

2004-11-02

arxiv.org/abs/math-ph/0411009v1

J.Nonlin.Math.Phys. 12 (2005) S86-S96

Physics

Mathematical Physics

11 pages, 2 figures. Contribution to a special issue of Journal of Nonlinear Mathematical Physics in honour of Francesco Calog

Scientific paper

We obtain lower bounds on the ground state energy, in one and three
dimensions, for the spinless Salpeter equation (Schr\"odinger equation with a
relativistic kinetic energy operator) applicable to potentials for which the
attractive parts are in $L^p(\R^n)$ for some $p>n$ ($n=1$ or 3). An extension
to confining potentials, which are not in $L^p(\R^n)$, is also presented.

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