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The method of Hill determinants in PT-symmetric quantum mechanics

Miloslav Znojil
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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.

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Miloslav Znojil. 2004-10-04. The method of Hill determinants in PT-symmetric quantum mechanics. https://arxiv.org/abs/math-ph/0410009

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