dorsal/arxiv
View SchemaCalculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution
| Authors | Ido Gilary, Avner Fleischer, Nimrod Moiseyev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507243 |
| URL | https://arxiv.org/abs/quant-ph/0507243 |
| DOI | 10.1103/PhysRevA.72.012117 |
Abstract
The solutions of the time independent Schrodinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L^2 methods that originally have been developed for the calculations of bound states. The existing non-Hermitian formalism breaks down when dealing with wavepackets(WP). An open question is how time dependent expectation values can be calculated when the Hamiltonian is NH ? Using the F-product formalism, which was recently proposed, [J. Phys. Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of different observable quantities for a simple well known study test case model Hamiltonian. We carry out a comparison between these results with those obtained from conventional(i.e., Hermitian) quantum mechanics (QM) calculations. The remarkable agreement between these results emphasizes the fact that in the NH-QM, unlike standard QM, there is no need to split the entire space into two regions; i.e., the interaction region and its surrounding. Our results open a door for a type of WP propagation calculations within the NH-QM formalism that until now were impossible.
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"abstract": "The solutions of the time independent Schrodinger equation for non-Hermitian\n(NH) Hamiltonians have been extensively studied and calculated in many\ndifferent fields of physics by using L^2 methods that originally have been\ndeveloped for the calculations of bound states. The existing non-Hermitian\nformalism breaks down when dealing with wavepackets(WP). An open question is\nhow time dependent expectation values can be calculated when the Hamiltonian is\nNH ? Using the F-product formalism, which was recently proposed, [J. Phys.\nChem., 107, 7181 (2003)] we calculate the time dependent expectation values of\ndifferent observable quantities for a simple well known study test case model\nHamiltonian. We carry out a comparison between these results with those\nobtained from conventional(i.e., Hermitian) quantum mechanics (QM)\ncalculations. The remarkable agreement between these results emphasizes the\nfact that in the NH-QM, unlike standard QM, there is no need to split the\nentire space into two regions; i.e., the interaction region and its\nsurrounding. Our results open a door for a type of WP propagation calculations\nwithin the NH-QM formalism that until now were impossible.",
"arxiv_id": "quant-ph/0507243",
"authors": [
"Ido Gilary",
"Avner Fleischer",
"Nimrod Moiseyev"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.012117",
"title": "Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution",
"url": "https://arxiv.org/abs/quant-ph/0507243"
},
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