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The One-dimensional Fractional Supersymmetric Quantum Mechanical Operator of Momentum

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Abstract

In the case of the quantum generalization of stable Lévy processes, expressions for the Hermitian operator of momentum and its eigenfunctions are proposed. The normalization constant has been determined and its relation to the translation operator is shown. The interrelation between the momentum and the wave number has been generalized for the processes with a non-integer dimensionality α. The simplest nonlocal superalgebra is introduced.

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Authors and Affiliations

  1. Department of Physics, Faculty of Fundamental Sciences, Vilnius Gediminas Technical University, Sauletekio Ave. 11, 10223, Vilnius, Lithuania

    Paulius Miškinis

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  1. Paulius Miškinis
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Correspondence to Paulius Miškinis.

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Miškinis, P. The One-dimensional Fractional Supersymmetric Quantum Mechanical Operator of Momentum. Appl Categor Struct 16, 213–221 (2008). https://doi.org/10.1007/s10485-007-9091-6

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  • DOI: https://doi.org/10.1007/s10485-007-9091-6

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