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Deformation of quantum mechanics in fractional-dimensional space

A. Matos-Abiague
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Abstract

A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way and quite analogous to their corresponding one-dimensional partners. Two simple systems, the free particle and the harmonic oscillator in fractional- dimensional spaces are reconsidered into the framework of the D-deformed quantum mechanics. Confined states in a D-deformed quantum well are studied. D-deformed coherent states are also found.

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A. Matos-Abiague. 2001-07-24. Deformation of quantum mechanics in fractional-dimensional space. https://doi.org/10.1088/0305-4470%2F34%2F49%2F321

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