J. Phys. A: Math. Theor. 48, 40FT01(2015), Sep 14, 2015
We generalize the Milne quantization condition to non-Hermitian systems. In the general case the ... more We generalize the Milne quantization condition to non-Hermitian systems. In the general case the underlying nonlinear Ermakov-Milne-Pinney equation needs to be replaced by a nonlinear integral differential equation. However, when the system is PT-symmetric or/and quasi/pseudo-Hermitian the equations simplify and one may employ the original energy integral to determine its quantization. We illustrate the working of the general framework with the Swanson model and two explicit examples for pairs of supersymmetric Hamiltonians. In one case both partner Hamiltonians are Hermitian and in the other a Hermitian Hamiltonian is paired by a Darboux transformation to a non-Hermitian one.
IOPscience is a unique platform for IOP-hosted journal content providing site-wide electronic acc... more IOPscience is a unique platform for IOP-hosted journal content providing site-wide electronic access to more than 130 years of leading scientific research, and incorporates some of the most innovative technologies to enhance your user-experience.
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and The... more This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of Pseudo Hermitian Hamiltonians in Quantum Physics as featured in the conference '6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics', City University London, UK, July 16--18 2007 (http://www.staff.city.ac.uk/~fring/PT/). Invited speakers at that meeting as well as
J. Phys. A: Math. Theor. 48, 40FT01(2015), Sep 14, 2015
We generalize the Milne quantization condition to non-Hermitian systems. In the general case the ... more We generalize the Milne quantization condition to non-Hermitian systems. In the general case the underlying nonlinear Ermakov-Milne-Pinney equation needs to be replaced by a nonlinear integral differential equation. However, when the system is PT-symmetric or/and quasi/pseudo-Hermitian the equations simplify and one may employ the original energy integral to determine its quantization. We illustrate the working of the general framework with the Swanson model and two explicit examples for pairs of supersymmetric Hamiltonians. In one case both partner Hamiltonians are Hermitian and in the other a Hermitian Hamiltonian is paired by a Darboux transformation to a non-Hermitian one.
IOPscience is a unique platform for IOP-hosted journal content providing site-wide electronic acc... more IOPscience is a unique platform for IOP-hosted journal content providing site-wide electronic access to more than 130 years of leading scientific research, and incorporates some of the most innovative technologies to enhance your user-experience.
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and The... more This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to the subject of Pseudo Hermitian Hamiltonians in Quantum Physics as featured in the conference '6th International Workshop on Pseudo Hermitian Hamiltonians in Quantum Physics', City University London, UK, July 16--18 2007 (http://www.staff.city.ac.uk/~fring/PT/). Invited speakers at that meeting as well as
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