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

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 $x=s-\mathrm{i}\epsilon$. The shift $\epsilon >0$ 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 $\mathcal{O}(g^{-1/4})$ 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.

13 pages, 3 figures

References in corpus (2)

• Making Sense of Non-Hermitian Hamiltonians
• The ODE/IM Correspondence

Cited by in corpus (1)

• Ad hoc physical Hilbert spaces in Quantum Mechanics