Abstract
We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interactions we depict solutions for the Coulomb potential of a point-like nucleus as well as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify peculiarities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field.
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