Abstract
The L2-scalar product ∫ Φ* (x) Ψ (x) d3x is not appropriate for the space of states describing the center-of-mass relative motion of two relativistic particles whose interaction is given by an energy-dependent quasipotential. The problem already appears in the relativistic quantum mechanics of a Klein-Gordon charged particle in an external field. We extend the methods developed for that case to study a two-particle system with an energy-independent scalar interaction as well as the relativistic Coulomb problem. We write down a Poincare invariant inner product for which the eigenfunctions corresponding to different energy eigenvalues are orthogonal. We also construct a perturbative expansion for bound-state energy eigenvalues, corresponding to an arbitrary energy-dependent (quasipotential) correction to an unperturbed Hamiltonian with a known spectrum. The description of observables and transition probabilities for eigenvalue problems with a polynomial dependence on the spectral parameter is also discussed.
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