Fractional Heisenberg Equation
نویسنده
چکیده
Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h̄)[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/h̄)[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. PACS: 03.65.-w; 03.65.Ca; 45.10.Hj; 03.65.Db
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