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arXiv · 0804.0586

Fractional Heisenberg Equation

Vasily E. Tarasov
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Abstract

Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[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 paper, we consider a fractional derivative on a set of quantum observables as a fractional power of the commutator (i/h)[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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Vasily E. Tarasov. 2008-04-03. Fractional Heisenberg Equation. https://doi.org/10.1016/j.physleta.2008.01.037

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