Exact Isospectral Pairs of PT-Symmetric Hamiltonians

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dc.creatorBender, Carl M.
dc.creatorHook, Daniel W.
dc.date2008-02-20
dc.date2008-04-27
dc.date.accessioned2026-07-07T11:40:22Z
dc.date.available2026-07-07T11:40:22Z
dc.descriptionA technique for constructing an infinite tower of pairs of PT-symmetric Hamiltonians, $\hat{H}_n$ and $\hat{K}_n$ (n=2,3,4,...), that have exactly the same eigenvalues is described. The eigenvalue problem for the first Hamiltonian $\hat{H}_n$ of the pair must be posed in the complex domain, so its eigenfunctions satisfy a complex differential equation and fulfill homogeneous boundary conditions in Stokes' wedges in the complex plane. The eigenfunctions of the second Hamiltonian $\hat{K}_n$ of the pair obey a real differential equation and satisfy boundary conditions on the real axis. This equivalence constitutes a proof that the eigenvalues of both Hamiltonians are real. Although the eigenvalue differential equation associated with $\hat{K}_n$ is real, the Hamiltonian $\hat{K}_n$ exhibits quantum anomalies (terms proportional to powers of $\hbar$). These anomalies are remnants of the complex nature of the equivalent Hamiltonian $\hat{H}_n$. In the classical limit in which the anomaly terms in $\hat{K}_n$ are discarded, the pair of Hamiltonians $H_{n,classical}$ and $K_{n,classical}$ have closed classical orbits whose periods are identical.
dc.description18 pages, 12 figures
dc.identifierhttps://arxiv.org/abs/0802.2910
dc.identifierhttp://arxiv.org/abs/0802.2910
dc.identifierJ.Phys.A41:244005,2008
dc.identifierdoi:10.1088/1751-8113/41/24/244005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/200234
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Physics
dc.titleExact Isospectral Pairs of PT-Symmetric Hamiltonians
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