Solution of the discretised time dependent Schr¨odinger equation for quantum dots subject to magnetic fields of arbitrary strength

Mukherjee, Urvi (2025) Solution of the discretised time dependent Schr¨odinger equation for quantum dots subject to magnetic fields of arbitrary strength. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (Urvi Mukherjee (20MS191)) 20MS191_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (9MB)

Abstract

The spectra of atoms and molecules greatly change in the presence of magnetic fields. Although extensive experimental investigations of quantum dots in magnetic fields have been conducted, a thorough computational framework remains to be developed. Traditional methods have limited application for large systems and in the presence of strong external perturbations. For magnetic fields, the property of gauge invariance must be ensured. This thesis investigates the quantum mechanical eigenvalues and eigenfunctions of an electron confined in a quantum dot under the influence of a uniform perpendicular magnetic field. This is done by constructing the appropriate Hamiltonian of the system in the presence of a magnetic field to ensure gauge invariance, and then solving the equations numerically. The imaginary time evolution method is used as a computational tool to overcome the aforementioned drawbacks. It proves to be a robust, versatile, and reliable method.

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