WKB Approximation with Conformable Operator

TL;DR

This paper extends the WKB approximation to conformable Hamiltonian systems using fractional order operators, providing a new method for analyzing quantum systems with conformable derivatives.

Contribution

The paper introduces a novel extension of the WKB method for conformable Hamiltonian systems with fractional derivatives, including derivation and illustrative examples.

Findings

Conformable WKB approximation aligns with traditional results when ppa=1.

The method effectively handles slowly varying potentials in conformable systems.

Illustrative examples demonstrate the applicability of the extended WKB approach.

Abstract

In this paper, the WKB method is extended to be applicable for conformable Hamiltonian systems where the concept of conformable operator with fractional order $\alpha$ is used. The WKB approximation for the $\alpha$-wavefunction is derived when the potential is slowly varying in space. The paper is furnished with some illustrative examples to demonstrate the method. The quantities of the conformable form are found to be inexact agreement with traditional quantities when $\alpha=1$.