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The propagation method can be used to describe a particle with wave character moving in an arbitrary one-dimensional potential, . This is done by approximating the potential as a series of potential steps. For a particle of energy incident from the left, transmission and reflection at the first step is calculated along with phase accumulated propagating to the step and expressed as a matrix.
Featuring new coverage of quantum engineering and quantum information processing, the third edition of this bestselling textbook continues to provide a uniquely practical introduction to the fundamentals of quantum mechanics. It features straightforward explanations of quantum effects, suitable for readers from all backgrounds; real-world engineering problems showcasing the practical application of theory to practice, providing a relevant and accessible introduction to cutting-edge quantum applications; over 60 accessible worked examples using MATLAB (as well as open-source Python), allowing deepened understanding through computational exploration and visualization; and a new chapter on quantum engineering, introducing state-of-the-art concepts in quantum information processing and quantum device design. Updated throughout and supported online by downloadable MATLAB code, exam questions, and solutions to over 150 homework problems for instructors, this is the ideal textbook for senior undergraduate and graduate students in applied science, applied physics, engineering, and materials science studying a first course in quantum mechanics.
According to the Schrödinger equation, a particle with wave character and mass in the presence of a potential may be described as a state that is a function of space and time. Space and time are assumed to be smooth and continuous. The potential can localize the particle to one region of space forming a bound state.
Quantum mechanics is a very successful description of atomic scale systems. The mathematical formalism relies on the algebra of noncommuting linear Hermitian operators. Postulates provide a logical framework with which to make contact with the results of experimental measurements.
It is possible to engineer properties of materials, devices, and systems by changing experimentally available control parameters to optimally approach a specific objective. The following sections demonstrate some potential applications of quantum engineering and show how this may be achieved by the development of efficient physical models combined with optimization algorithms.
In classical mechanics, the constants of motion of an isolated system are energy, linear momentum, and angular momentum. So far in this book, angular momentum has not been considered. This chapter starts by defining classical angular momentum and then proceeds to find the corresponding quantum operators. Following this, a hydrogenic atom is studied as a prototype application.
Engineers who design transistors, lasers, and other semiconductor components want to understand and control the cause of resistance to current flow so that they may better optimize device performance. A detailed microscopic understanding of electron motion from one part of a semiconductor to another requires the explicit calculation of electron scattering probability. One would like to know how to predict electron scattering from one state to another – something quantum mechanics can do.