Quantum Reports (Aug 2022)

Schrödinger Equation with Geometric Constraints and Position-Dependent Mass: Linked Fractional Calculus Models

  • Ervin K. Lenzi,
  • Luiz R. Evangelista,
  • Haroldo V. Ribeiro,
  • Richard L. Magin

DOI
https://doi.org/10.3390/quantum4030021
Journal volume & issue
Vol. 4, no. 3
pp. 296 – 308

Abstract

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We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which are given in terms of stretched exponential functions. The results can be linked to the properties of the system and show anomalous spreading for the wave packet. We also analyze the interplay between the backbone structure with branches constraining the different directions and the effective mass. In particular, we show how a fractional Schrödinger equation emerges from this scenario.

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