Fractional Heisenberg equation |
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Authors: | Vasily E Tarasov |
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Institution: | Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia |
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Abstract: | Fractional derivative can be defined as a fractional power of derivative. The commutator (i/?)H,⋅], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule. In this Letter, we consider a fractional derivative on a set of quantum observables as a fractional power of the commutator (i/?)H,⋅]. As a result, we obtain a fractional generalization of the Heisenberg equation. The fractional Heisenberg equation is exactly solved for the Hamiltonians of free particle and harmonic oscillator. The suggested Heisenberg equation generalize a notion of quantum Hamiltonian systems to describe quantum dissipative processes. |
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Keywords: | 03 65 -w 03 65 Ca 45 10 Hj 03 65 Db |
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