Continuum solutions to the two–center Coulomb problem in prolate spheroidal coordinates

We present a computational and theoretical framework for solving the Schrödinger equation (SE) for the two–center Coulomb problem in prolate spheroidal coordinates when the energy of the SE is positive. A general and robust computer code has been produced that calculates the separation constants, spheroidal harmonic expansion coefficients, regular quasi–radial two–center Coulomb wave functions, and two–center Coulomb phase shifts. These quantities can be calculated over a range of internuclear separations, angular momentum projections, and continuum electron momenta. A representative set of results are presented and compared with previous calculations, excellent agreement is found in many cases while significant disagreements are found in others.