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<p>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 Schrödinger 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月12日

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  • Paolo Amore,
  • Francisco M. Fernández

摘要

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 Schrödinger 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.