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ABSTRACT
The Schrödinger-Poisson equation, a connected set of partial differential equations, allows us to understand the behavior of charged particles, notably electrons, in quantum-confined systems vulnerable to electrostatic potentials. This thesis focuses on the Finite Element Method (FEM) for the Schrödinger-Poisson equation solution. The objective of the study is to get a thorough understanding of the quantum phenomena displayed by confined charge carriers and their implications for semiconductor device applications. The first section of this research is a thorough analysis of the theory behind the SchrödingerPoisson equation, including the Poisson's equation, the time-dependent Schrödinger equation, and the interaction between quantum mechanics and electrostatics. The fundamental ideas of the finite element method are introduced, with an emphasis on the method's prowess in dealing with issues with complicated boundary conditions.
