## 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.

http://arxiv.org/abs/1401.1435
Quantum Physics (quant-ph)