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• W2891851372 abstract "We touch upon a long-standing question of the “true” one-dimensional hydrogen atom solution. From a symmetry point of view, the Kepler problem in the d ≥ 2 dimension is characterized by geometrical rotational symmetry, SO(d), as well as dynamical “accidental” SO(d + 1) symmetry. Because of the topology, these two symmetries are mutually exclusive in one dimension, regardless of the regularization employed, drawing one to a conclusion that the question of the “true” hydrogen atom in one dimension does not have an answer because a single dimension cannot support both of the symmetries of the Kepler problem. We argue our findings using a novel method to recover and classify solutions appearing in the literature according to the symmetry they respect. In particular, curious features of some of the solutions—double degeneracy and particle confinement—are directly attributed to the dynamical symmetry behind them." @default.
• W2891851372 created "2018-09-27" @default.
• W2891851372 creator A5061065769 @default.
• W2891851372 date "2018-10-01" @default.
• W2891851372 modified "2023-09-24" @default.
• W2891851372 title "On the symmetry of a one-dimensional hydrogen atom" @default.
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• W2891851372 doi "https://doi.org/10.1063/1.5028500" @default.
• W2891851372 hasPublicationYear "2018" @default.
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