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The Large −g Observability of the Low-Lying Energies in the Strongly Singular Potentials V (x) = x 2 + g 2/x 6 after their 𝓟T −symmetric Regularization

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Abstract

The elementary quadratic plus inverse sextic interaction V (x) = x 2 + g 2/x 6 containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate x = s −iε. The shift ε > 0 is fixed while the value of s is kept real and potentially observable, s ∈ (−∞, ∞). The low-lying energies of bound states are found in closed form for the large couplings g ≫ 1. Within the asymptotically vanishing 𝒪(g −1/4) error bars these energies are real so that the time-evolution of the system may be expected unitary in an ad hoc physical Hilbert space.

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Acknowledgement

Discussions of the subject with Roberto Tateo and with several other colleagues are gratefully appreciated.

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  1. Nuclear Physics Institute ASCR, 250 68 Řež, Czech Republic

    Miloslav Znojil

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  1. Miloslav Znojil
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Correspondence to Miloslav Znojil.

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Znojil, M. The Large −g Observability of the Low-Lying Energies in the Strongly Singular Potentials V (x) = x 2 + g 2/x 6 after their 𝓟T −symmetric Regularization. Int J Theor Phys 53, 2549–2557 (2014). https://doi.org/10.1007/s10773-014-2052-6

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  • DOI: https://doi.org/10.1007/s10773-014-2052-6

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