Complex Square Well --- A New Exactly Solvable Quantum Mechanical Model

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dc.creatorBender, Carl M.
dc.creatorBoettcher, Stefan
dc.creatorJones, H. F.
dc.creatorSavage, Van M.
dc.date1999-06-16
dc.date.accessioned2026-07-07T10:55:13Z
dc.date.available2026-07-07T10:55:13Z
dc.descriptionRecently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^ε$ was studied. It was found that the energy levels for this theory are real for all $ε\geq0$. Here, the limit as $ε\to\infty$ is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, $H=p^2+x^{2M}(ix)^ε$ (M=1,2,3,...) is also studied, and this PT-symmetric Hamiltonian becomes exactly solvable in the large-εlimit as well. In effect, what is obtained in each case is a complex analog of the Hamiltonian for the square well potential. Expansions about the large-εlimit are obtained.
dc.description7 pages, Revtex, 2 eps-figures enclosed
dc.identifierhttps://arxiv.org/abs/quant-ph/9906057
dc.identifierhttp://arxiv.org/abs/quant-ph/9906057
dc.identifierJ.Phys.A32:6771-6781,1999
dc.identifierdoi:10.1088/0305-4470/32/39/305
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/186045
dc.subjectQuantum Physics
dc.subjectCondensed Matter
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleComplex Square Well --- A New Exactly Solvable Quantum Mechanical Model
dc.typetext

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