Abstract
We have studied the solutions of a wave equation which describes a spin-zero particle in the Coulomb field of a nucleus. An interesting feature of this equation is that the kernel is not of the Fredholm type. The behavior of the momentum space wavefunction for large momentum is not determined solely by the angular momentum state but, as in the cases of the Dirac and Klein-Gordon equations, it depends on the electric charge as well. Our analysis of the asymptotic properties is based on a Mellin transformation of the momentum space equation. This leads to a singular integral equation with a Cauchy-type kernel which may be treated by standard methods. The equation is shown to have unique solutions.
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