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arXiv:quant-ph/9906057 · Journal of Physics A Mathematical and General

Complex square well - a new exactly solvable quantum mechanical model

Carl M. Bender, Stefan Boettcher, Hugh F Jones, Van M. Savage

Published Sep 15, 1999• 60 citations
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Abstract

Recently, a class of -invariant quantum mechanical models described by the non-Hermitian Hamiltonian H = p 2 + x 2 (i x ) was studied. It was found that the energy levels for this theory are real for all 0. Here, the limit as is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p 2 + x 2 M (i x ) ( M = 1,2,3, ... ) is also studied, and this -symmetric Hamiltonian becomes exactly solvable in the large- limit as well. In effect, what is obtained in each case is a complex analogue of the Hamiltonian for the square-well potential. Expansions about the large- limit are obtained.

DOI
10.1088/0305-4470/32/39/305

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