Exploring Fractional Quantum Mechanics: Stability Analysis and Wave Propagation in Coupled Schrödinger Equations

Fractional Quantum Mechanics (FQM) has emerged as a fascinating theoretical framework extending traditional quantum mechanics to describe physical systems with non-local or long-range interactions. In this paper, we delve into the realm of FQM, focusing on stability analysis and wave propagation in coupled Schrödinger equations. We begin with a comprehensive overview of FQM, elucidating its fundamental principles and mathematical formalism. Subsequently, we conduct stability analysis of coupled fractional Schrödinger equations, exploring the conditions under which these systems exhibit stable behavior. Furthermore, we investigate wave propagation phenomena within such systems, shedding light on the unique characteristics of fractional quantum waves. Our findings not only contribute to advancing the theoretical understanding of FQM but also offer insights into potential applications in diverse fields ranging from condensed matter physics to quantum information processing.