The hydrogen atom inside boxes with paraboloidal surfaces

摘要

The Schrouml;dinger equation for the hydrogen atom inside boxes defined by pairs of confocal, coaxial and mutually intersecting paraboloidal walls is solved exactly using parabolic coordinates. The energy eigenvalues and eigenfunctions for the lowest states of the system are determined numerically for such boxes, having different sizes and shapes. Also, the isotropic and anisotropic components of the hyperfine splitting are evaluated.