Analytic solution for a class of multiscale long-range potentials Article Swipe
Haixiang Fu
,
Xiaoji Zhou
,
Mingzhe Li
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1103/b8sh-1dk4
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.1103/b8sh-1dk4
We present a unified exact analytic solution of the radial Schrödinger equation with a class of four long-range potentials, three of which are two-scale. The physics of different potentials are encapsulated in the solution variable and parameters. Based on this solution and its asymptotic behaviors, we generalize Bo Gao’s formulation of quantum defect theory for single-scale potentials to two-scale regime. As an application of this two-scale quantum defect theory, we propose a concept of harmonic oscillator quantum defect of energy levels in a spherical harmonic trap, which characterizes the effect of the two-body interactions on their trap states. This concept is a generalization of the standard quantum defect for Coulomb potential, with a distinct feature that the equations followed by the two types of quantum defects induced by the potentials under study are formally the same yet with different parameters. Examples of these two quantum defects are illustrated for Rb and Cs atoms.
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- OA Status
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- References
- 48
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https://openalex.org/W4415492844Canonical identifier for this work in OpenAlex
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Analytic solution for a class of multiscale long-range potentialsWork title
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articleOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-09-17Full publication date if available
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Haixiang Fu, Xiaoji Zhou, Mingzhe LiList of authors in order
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goldOpen access status per OpenAlex
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