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We revisit the quantum-mechanical two-dimensional hydrogen atom with anelectric field confined to a circular box of impenetrable wall. In order toobtain the energy spectrum we resort to the Rayleigh-Ritz method with apolynomial basis sets. We discuss the limits of large and small box radius andthe symmetry of the solutions of the Schr\"{o}dinger equation. An interestingfeature of the model is the appearance of accidental degeneracy and thesplitting of degenerate energy levels due to the presence of the electricfield.

On the two-dimensional hydrogen atom in a circular box in the presence of an electric field