Hydrogen atom in a spherical box. II. Effect on hyperfine energy of excited state admixture On the hyperfine splitting of the hydrogen atom in a spherical box

We formulate the exact solution of the Schrödinger equation for systems of one electron in the Coulomb field of one or two fixed nuclei at the foci inside prolate spheroidal boxes. Numerical results are obtained for the energy eigenvalues and eigenfunctions of the lowest states of the hydrogen atom and the H+2 and HeH++ molecular ions for boxes of different sizes and eccentricities. We also evaluate the hyperfine splitting of atomic hydrogen and of H+2.

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ABSTRACT:The separability of the Schrö dinger equation for harmonic oscillators in D dimensions and in different coordinate systems (Cartesian, circular, spherical) makes possible the construction of common generating functions for the complete harmonic oscillator wave functions in the corresponding dimensions and coordinates. Explicit forms of such generating functions and their series expansions are presented, and one of their applications is illustrated through the evaluation of transformation brackets.