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arXiv · 0907.2699

Weyl Quantization of Fractional Derivatives

Vasily E. Tarasov
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Abstract

The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives. To obtain the quantum analogs of fractional Riemann-Liouville derivatives, which are defined on a finite interval of the real axis, we use a representation of these derivatives for analytic functions. To define a quantum analog of the fractional Liouville derivative, which is defined on the real axis, we can use the representation of the Weyl quantization by the Fourier transformation.

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Vasily E. Tarasov. 2009-07-15. Weyl Quantization of Fractional Derivatives. https://doi.org/10.1063/1.3009533

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