Abstract
Abstract An interdimensional degeneracy linking the orbital angular momentum projection |m| and spatial dimension D yields D-dimensional eigenstates for H2+ by simple correspondence with suitably scaled D = 3 excited states. The wave-equation for fixed nuclei is separable in D-dimensional spheroidal coordinates, giving generalized two-center differential equations with parametric dependence on the internuclear distance R. A computer program is presented which is capable of calculating the two eigenparameters, the energy ED(R), and the separation constant AD(R) related to the total orbital angular momentum and the Runge-Lenz vector, to high accuracy over a large range in R for dimensions up to D = 100, or equivalently, for projections up to |m| = 50 for D = 3. The program can be implemented on personal computers to give accuracies up to 16 digits. The execution times required are modest. Normalization constants, wavefunctions and expectation values can be calculated as well, but at a cost of much larger execution times for even moderate accuracy.
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