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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Poster (joint session MP/QI)

MP 7.2: Poster

Dienstag, 19. März 2024, 11:00–13:00, Poster B

Quantum Dynamics on a Two-dimensional Comb: A Numerical Investigation — •Ognen Kapetanoski and Irina Petreska — Ss. Cyril and Methodius University in Skopje, Faculty of Natural Sciences and Mathematics, Institute of Physics, Skopje, Macedonia

This study explores the quantum dynamics in anisotropic and heterogeneous media, using the comb model - a unique branched structure characterized by a backbone and lateral fingers. The focus is on the two-dimensional comb, which constitutes a simplified yet comprehensive model for theoretical investigation of the quantum motion under geometric constraints. The comb-like constraints are achieved by incorporating the Dirac delta function into the kinetic energy operator of the Schrödinger equation. Employing the finite difference approximation and the fourth-order Runge-Kutta method, the time-dependent Schrödinger equation is numerically solved. This enables the calculation of the wave functions and analysis of the probability density function. From the obtained results, localization of the wave packet due to the comb-like geometric constraints is evident. We also recall the previously derived analytical solutions on an infinite domain, expressed in terms of the Fox H-function. The comparative analysis between the analytical and numerical solution highlights the complexity of quantum transport phenomena, underscoring the challenges and potential of theoretical and computational approaches in quantum mechanics.

[1] T. Sandev, I. Petreska, E.K. Lenzi, J. Math. Phys. 59, 012104 (2018).

Keywords: Schrödinger equation; comb model; numerical methods