The Fractionary Schr\"{o}dinger Equation, Green Functions and Ultradistributions

TL;DR

This paper extends the Fractionary Schrödinger Equation using Tempered Ultradistributions, providing new methods to evaluate Green's functions for particles with arbitrary derivative orders.

Contribution

It introduces a novel application of Tempered Ultradistributions to the Fractionary Schrödinger Equation, enabling the calculation of Green's functions for arbitrary fractional orders.

Findings

Green's function for a free particle with arbitrary fractional order derived

Demonstrates the use of Tempered Ultradistributions in quantum mechanics

Provides examples illustrating the generalized approach

Abstract

In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green's function for a free particle in the general case, for an arbitrary order of the derivative index.