Metric versus observable operator representation, higher spin models

Abstract

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schroedinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the nonlinear Ermakov-Pinney equation.

13 pages

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Cited by in corpus (12)

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• Eternal life of entropy in non-Hermitian quantum systems
• Solvable two dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems
• Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators
• Quasi-exactly solvable quantum systems with explicitly time-dependent Hamiltonians
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Time-dependent C-operators as Lewis-Riesenfeld invariants in non-Hermitian theories
• Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
• Relativistic Ermakov-Milne-Pinney Systems and First Integrals