dorsal/arxiv
View SchemaDiagonalization of Hamiltonians, uncertainty matrices and Robertson inequality
| Authors | D. A. Trifonov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012044 |
| URL | https://arxiv.org/abs/quant-ph/0012044 |
| Journal | In "Geometry, Integrability and Quantization", eds: I.Mladenov and G.Naber (Coral Press, 2001) pp. 294-312 |
Abstract
The problem of diagonalization of Hamiltonians of N-dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator of time-dependent CT which can transform any Hamiltonian to that of a system of uncoupled stationary oscillators is constructed. The close relationship between methods of canonical transformations, time-dependent integrals of motion and dynamical symmetry is noted. The diagonalization and symplectic properties of the uncertainty matrix for 2N canonical observables are studied. It is shown that the normalized uncertainty matrix is symplectic for the squeezed multimode Glauber coherent states and for the squeezed Fock states with equal photon numbers in each mode. The Robertson uncertainty relation for the dispersion matrix of canonical observables is shown to be minimized in squeezed coherent states only.
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"abstract": "The problem of diagonalization of Hamiltonians of N-dimensional boson systems\nby means of time-dependent canonical transformations (CT) is considered, the\ncase of quadratic Hamiltonians being treated in greater detail. The unitary\ngenerator of time-dependent CT which can transform any Hamiltonian to that of a\nsystem of uncoupled stationary oscillators is constructed. The close\nrelationship between methods of canonical transformations, time-dependent\nintegrals of motion and dynamical symmetry is noted.\n The diagonalization and symplectic properties of the uncertainty matrix for\n2N canonical observables are studied. It is shown that the normalized\nuncertainty matrix is symplectic for the squeezed multimode Glauber coherent\nstates and for the squeezed Fock states with equal photon numbers in each mode.\nThe Robertson uncertainty relation for the dispersion matrix of canonical\nobservables is shown to be minimized in squeezed coherent states only.",
"arxiv_id": "quant-ph/0012044",
"authors": [
"D. A. Trifonov"
],
"categories": [
"quant-ph"
],
"journal_ref": "In \"Geometry, Integrability and Quantization\", eds: I.Mladenov and\n G.Naber (Coral Press, 2001) pp. 294-312",
"title": "Diagonalization of Hamiltonians, uncertainty matrices and Robertson inequality",
"url": "https://arxiv.org/abs/quant-ph/0012044"
},
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