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Chemical Physics Letters

Representation of one-dimensional motion in a morse potential by a quadratic hamiltonian

Raphael David Levine

Published Feb 1, 1983• 127 citations
Publisher
DOI
10.1016/0009-2614(83)85071-4

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We analyse a class of non-Hermitian quadratic Hamiltonians, which are of the form , where α, β are real constants, with α ≠ β, and and are generalized creation and annihilation operators respectively. Thus, these Hamiltonians may be classified as generalized Swanson models. It is shown that the eigenenergies are real for a certain range of values of the parameters. A similarity transformation ρ, mapping the non-Hermitian Hamiltonian H to a Hermitian one h , is also obtained. It is shown that H and h share identical energies. As explicit examples, the solutions of a couple of models based on the trigonometric Rosen–Morse I and the hyperbolic Rosen–Morse II type potentials are obtained. We also study the case where the non-Hermitian Hamiltonian is symmetric.