PT-invariant one-dimensional Coulomb problem
Abstract
The one-dimensional Coulomb-like potential with a real coupling constant beta, and a centrifugal-like core of strength G = alpha2 - 1/4, viz. V(x) = alpha2 - (1/4)/(x-ic)2 + beta/|x-ic|, is discussed in the framework of PT-symmetry. The PT-invariant exactly solvable model so formed, is found to admit a double set of real and discrete energies, numbered by a quasi-parity q = +/- 1.
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