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The time independent fractional Schrödinger equation with position-dependent mass

Author

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  • Jamshir, Narges
  • Lari, Behzad
  • Hassanabadi, Hassan

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.

Suggested Citation

  • Jamshir, Narges & Lari, Behzad & Hassanabadi, Hassan, 2021. "The time independent fractional Schrödinger equation with position-dependent mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    • Handle: RePEc:eee:phsmap:v:565:y:2021:i:c:s0378437120309146
    DOI: 10.1016/j.physa.2020.125616
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    Cited by:

    1. Tehrani, D. Haji Taghi & Solaimani, M., 2023. "Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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