2025/04/26 by Paolo Amore, Amore, Paolo, Francisco M. Fernández +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2504.18928
openalex publication_date 2025/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.