Spinless Salpeter Equation: Analytic Results

The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic statements on resulting solutions. In view of this rather unsatisfactory state of affairs, we calculate analyic upper bounds on the involved energy levels, and, for the Coulomb potential, on the ground-state energy at the critical value of the coupling constant.