Canonical and perturbed quantum potential-well problems: a universal function approach

Ahmed, I 2007, Canonical and perturbed quantum potential-well problems: a universal function approach, Masters by Research, Electrical and Computer Engineering, RMIT University.


Document type: Thesis
Collection: Theses

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Title Canonical and perturbed quantum potential-well problems: a universal function approach
Author(s) Ahmed, I
Year 2007
Abstract The limits of the current micro-scale electronics technology have been approaching rapidly. At nano-scale, however, the physical phenomena involved are fundamentally different than in micro-scale. Classical and semi-classical physical principles are no longer powerful enough or even valid to describe the phenomena involved. The rich and powerful concepts in quantum mechanics have become indispensable. There are several commercial software packages already available for modeling and simulation of the electrical, magnetic, and mechanical characteristics and properties of the nano-scale devices. However, our objective here is to go one step further and create a physics-based problem-adapted solution methodology. We carry out computation for eigenfunctions of canonical and the associated perturbed quantum systems and utilize them as co-ordinate functions for solving more complex problems. We have profoundly worked with the infinite quantum potential-well problem, since they have closed-form solutions and therefore are analytically known eigenfunctions. Perturbation of the infinite quantum potential-well was done through a single box function, multiple box functions, and with a triangular function. The proposed solution concept utilizes the notion of "Universal Functions" previously introduced for solving complex engineering boundary value problems. Upon formulating our methodology we were able to generate numerical solutions of eigenvalues and eigenfunctions for our one and two dimensional perturbed problems. We were also able to tune the added potential and this illuminates the fact that, by creating arbitrary potentials, we succeeded in controlling the distribution of eigenvalue to a definite level and thu s achieved a certain degree of localization.
Degree Masters by Research
Institution RMIT University
School, Department or Centre Electrical and Computer Engineering
Keyword(s) Eigenvalues
Eigenvectors
Quantum electronics
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