Abstract

This paper presents a description of the abstractions required for the expression and solution of the linear single‐particle Schrödinger 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 Schrödinger 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.

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