A variational calculation for a hydrogen atom in a cylindrical cavity with a magnetic field shows that making the cutoff exponent an adjustable parameter improves ground-state energies.
On the two-dimensional hydrogen atom in a circular box in the presence of an electric field
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abstract
We revisit the quantum-mechanical two-dimensional hydrogen atom with an electric field confined to a circular box of impenetrable wall. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with a polynomial basis sets. We discuss the limits of large and small box radius and the symmetry of the solutions of the Schr\"{o}dinger equation. An interesting feature of the model is the appearance of accidental degeneracy and the splitting of degenerate energy levels due to the presence of the electric field.
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Cylindrically confined $H$ atom in magnetic field: variational cut-off factor
A variational calculation for a hydrogen atom in a cylindrical cavity with a magnetic field shows that making the cutoff exponent an adjustable parameter improves ground-state energies.