Bound states of PT-symmetric separable potentials

Carl M. Bender, Hugh F. Jones

All of the PT-symmetric potentials that have been studied so far have been local. In this paper nonlocal PT-symmetric separable potentials of the form \(V(x,y)=i\epsilon[U(x)U(y)-U(-x)U(-y)]\), where \(U(x)\) is real, are examined. Two specific models are examined. In each case it is shown that there is a parametric region of the coupling strength $\epsilon$ for which the PT symmetry of the Hamiltonian is unbroken and the bound-state energies are real. The critical values of \(\epsilon\) that bound this region are calculated.
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

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