The method of Hill determinants in PT-symmetric quantum mechanics

Abstract

Hill-determinant method is described and shown applicable within the so called PT-symmetric quantum mechanics. We demonstrate that in a way paralleling its traditional Hermitian applications and proofs the method guarantees the necessary asymptotic decrease of wave functions as resulting from a fine-tuned mutual cancellation of their asymptotically growing exponential components. Technically, the rigorous proof is needed/offered that in a quasi-variational spirit the method allows us to work, in its numerical implementations, with a sequence of truncated forms of the rigorous Hill-determinant power series for the normalizable bound states.