Bound state inequality from the spinless Salpeter equation with the Yukawa potential

Abstract

In this paper, we discuss the bound-state problem for the spinless Salpeter equation with the Yukawa potential. Due to the nonlocal term of the Hamiltonian encountered, we use the eigenfunction for the ground state of the hydrogen atom as a trial function and employ the variational method to solve the spinless Salpeter equation. We derive the upper bounds on the eigenvalues to obtain the bound state inequality. The constraint on the interaction strength α is given, (2.42m–1.32μ)μ/(2.37m2–mμ) ≤ α < 8/(3π). And the maximum of the screening parameter of the Yukawa potential μ is obtained, μ_max = 1.14 m.