Exemplifying Quantum Systems in a Finite Element Basis

This paper presents a description of the abstractions required for the expression and solution of the linear single-particle Schrodinger equation in a finite element basis. This paper consists of two disparate themes: First, to layout and establish the foundations of finite element analysis as an approximate numerical solution to extendable quantum mechanical systems; and second, to promote a high-performance open-source computational model for the approximate numerical solution to quantum mechanical systems. The structural foundation of the one- and two-dimensional time-independent Schrodinger equation describing an infinite potential well is explored and a brief overview of the hierarchal design of the computational library written in C++ is given.