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Beteiligte Max-Planck-Institute |
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MPI für extraterrestrische Physik |
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Autoren |
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Treumann, R. A. |
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Publikationstyp |
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Artikel |
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Titel |
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An attempt of formulating the principles of a generalized- lorentzian quantum mechanics |
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Zusammenfassung |
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We present a generalization of the quantum mechanical formalism to a class of propagators that is closely related to the generalized Lorentzian path integrals we proposed in an earlier publication [R. A. Treumann, Phys. Rev. E 57, 5150 (1998)] introducing a (real) control parameter kappa > 0. In this formulation the Schrodinger and Heisenberg formalisms assume a definite form when introducing a new kappa-Hamilton operator that is a functional of the quantum Hamiltonian operator. For kappa --> infinity the usual quantum mechanics is recovered. This approach though apparently successful for constant time suffers from violating the semi-group property of quantum operators. Currently we do not see how to cure this deficiency. We nevertheless present the idea to the public in the hope that a way may be found to handle this problem in the time domain. The formalism is formally applied to the harmonic oscillator. We define new creation and destruction operators, find their commutators, and calculate the eigenvalues of the new kappa- Hamilton operator. These eigenvalues turn out to become time- dependent, whatever this means. In addition the energy levels are not anymore equally spaced. It is believed that the theory may be of use in application to quantum chaos and quantum turbulence. |
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Quelle |
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Physica Scripta 66 (6), 417-424 (2002) |
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Sprache |
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English |
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Identifikation |
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ISI 000180374400003
ISSN 0031-8949 |
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© 2009, Max-Planck-Gesellschaft, München |
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