Levy Flights over Quantum Paths

TL;DR

This paper investigates how Levy flights influence quantum path integrals, deriving analytical kernels for free particles and particles in a box using Fox H-functions, thus extending quantum kernel formulations.

Contribution

It introduces new analytical expressions for quantum kernels affected by Levy flights, including a general formula and specific cases for free particles and particles in a box.

Findings

Derived the free particle kernel in terms of Fox H-function.

Obtained a new kernel equation for particles in a box.

Unified Levy flight effects with known quantum formulas.

Abstract

An impact of integration over the paths of the Levy flights on the quantum mechanical kernel has been studied. Analytical expression for a free particle kernel has been obtained in terms of the Fox H-function. A new equation for the kernel of a partical in the box has been found. New general results include the well known quantum formulae for a free particle kernel and particle in box kernel.