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

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 \(x=s−i\epsilon\). The shift \(\epsilon>0\) is fixed while the value of s is kept real and potentially observable, \(s∈(−\infty,\infty)\). The low-lying energies of bound states are found in closed form for the large couplings g. Within the asymptotically vanishing \(\mathcal{O}(g^{−1/4})\) 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.
Quantum Physics (quant-ph)

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