Year: 2026
Type: article
Abstract: We report a non-relativistic solution of the one-dimensional helium atom confined to the half-line r > 0. Using a variational product basis of Laguerre functions with dimension up to N = 45, we obtained convergence of the first four bound-state energies to six significant digits: -2.10839, -2.05037, -2.02901, and -2.01883 atomic units. Despite the theoretical spin and exchange-symmetry degeneracy, we observed a numerical anomaly in which the symmetric (singlet) states converge drastically more slowly than the antisymmetric (triplet) states, potentially requiring basis sizes exceeding N = 1000 to reach the same triplet energies. With N = 45, the symmetric energies converged only to the first four significant digits. The energy spectrum and wave function plots revealed a clear Rydberg-like ladder of two-electron configurations, characterized by a (1s, ns) nodal structure.
Author: Dmitry A. Konovalov
Institution: James Cook University
Language: English
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,890
Funder: James Cook University
OpenAlex ID: W7160277883
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