Ultradistributions and The Fractionary Schr\"{o}dinger Equation
A. L. De Paoli, M. C. Rocca
TL;DR
This paper extends the Fractionary Schrödinger Equation using Tempered Ultradistributions, providing new analytical tools and examples, including the calculation of the Green's function for a free particle.
Contribution
It introduces the application of Tempered Ultradistributions to the Fractionary Schrödinger Equation, offering novel analytical methods and explicit solutions.
Findings
Green's function for a free particle derived
Demonstrates the utility of ultradistributions in fractional quantum mechanics
Provides new examples of ultradistribution applications
Abstract
In this work, we generalize the results of Naber about the Fractionary Schr\"{o}dinger Equation with the use 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.
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Taxonomy
TopicsMathematical functions and polynomials · Fractional Differential Equations Solutions · Algebraic and Geometric Analysis