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 unsatisfactory state of affairs, we calculate analytic upper bounds on the involved energy levels, and, for the Coulomb potential, the ground-state energy at the critical coupling constant. Invited talk, presented by F. F. Schöberl, at the “XI International Conference: Problems of Quantum Field Theory,” at the Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, July 13–17, 1998, Dubna, Russia.