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The One-Dimensional Spinless Relativistic Coulomb Problem
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Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues. These upper bounds seem to disprove the previous explicit solution.
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Semirelativistic Bound States: (Pseudo-) Spinless-Salpeter Approaches Reassessed
A proceedings review that applies rigorous spectral bounds to semirelativistic Hamiltonians with generalized Hellmann potentials and warns against pseudo-spinless-Salpeter approximations.
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