The time independent fractional Schrödinger equation with position-dependent mass

Narges Jamshir, Behzad Lari and Hassan Hassanabadi

Physica A: Statistical Mechanics and its Applications, 2021, vol. 565, issue C

Abstract: In this paper, we present a fractional form of Schrödinger equation using the Kallil’s derivative method. Then we investigate the capability of this equation to obtain the wave functions and its energy levels for a particle trapped in infinite potential well (IPW) for the range1<α≤2. We also, present the fractional form of the Schrödinger equation for a particle with position-dependent mass (PDM) and by using it, we obtain wave functions and its energy levels in range 0 <α≤1 and in different amounts of η and μ in which μ + η = 1/2. It seems that our method is very useful to solve the problems in PDM case.

Keywords: Fractional derivatives; Fractional Schrödinger equation; Infinite well potential; Position dependent mass (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:565:y:2021:i:c:s0378437120309146

DOI: 10.1016/j.physa.2020.125616

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