Fractional WKB Approximation

TL;DR

This paper explores the extension of the WKB approximation to fractional systems using fractional calculus, proposing a new wave function construction and demonstrating its application through detailed examples.

Contribution

It introduces a fractional WKB approximation method with a novel wave function construction based on Hamilton's principle function.

Findings

Successful application to two example systems

Demonstrates the feasibility of fractional WKB approximation

Provides a foundation for future fractional quantum analyses

Abstract

Wentzel, Kramers, Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case the wave function is constructed such that the phase factor is the same as the Hamilton's principle function "S". To demonstrate our proposed approach two examples are investigated in details.