Deformation of quantum mechanics in fractional-dimensional space

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 in 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. (author)