dorsal/arxiv
View SchemaNon-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation
| Authors | Carla Figueira de Morisson Faria, Andreas Fring |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609096 |
| URL | https://arxiv.org/abs/quant-ph/0609096 |
| DOI | 10.1134/S1054660X07040196 |
| Journal | Laser Physics 17 (2007) 424-437 |
Abstract
We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of a non-Hermitian Hamiltonian and pay particular attention to the role played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate the general formalism with three explicit examples: i) the generalized Swanson Hamiltonians, which constitute non-Hermitian extensions of anharmonic oscillators, ii) the spiked harmonic oscillator, which exhibits explicit supersymmetry and iii) the -x^4-potential, which serves as a toy model for the quantum field theoretical phi^4-theory.
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"abstract": "We provide a reviewlike introduction into the quantum mechanical formalism\nrelated to non-Hermitian Hamiltonian systems with real eigenvalues. Starting\nwith the time-independent framework we explain how to determine an appropriate\ndomain of a non-Hermitian Hamiltonian and pay particular attention to the role\nplayed by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of\nsuch systems having in particular the question in mind of how to couple\nconsistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate\nthe general formalism with three explicit examples: i) the generalized Swanson\nHamiltonians, which constitute non-Hermitian extensions of anharmonic\noscillators, ii) the spiked harmonic oscillator, which exhibits explicit\nsupersymmetry and iii) the -x^4-potential, which serves as a toy model for the\nquantum field theoretical phi^4-theory.",
"arxiv_id": "quant-ph/0609096",
"authors": [
"Carla Figueira de Morisson Faria",
"Andreas Fring"
],
"categories": [
"quant-ph"
],
"doi": "10.1134/S1054660X07040196",
"journal_ref": "Laser Physics 17 (2007) 424-437",
"title": "Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation",
"url": "https://arxiv.org/abs/quant-ph/0609096"
},
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