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arXiv · 1401.1435

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

Miloslav Znojil
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Abstract

The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ is fixed while the value of $s$ is kept real and potentially observable, $s \in (-\infty,\infty)$. The low-lying energies of bound states are found in closed form for the large couplings $g$. Within the asymptotically vanishing ${\cal O}(g^{-1/4})$ error bars these energies are real so that the time-evolution of the system may be expected unitary in an {\em ad hoc} physical Hilbert space.

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Miloslav Znojil. 2014-01-24. 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. https://doi.org/10.1007/s10773-014-2052-6

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