Elementary Quantum Mechanics in One DimensionJHU Press, 22 okt 2004 - 229 pagina's One of the key components of modern physics, quantum mechanics is used in such fields as chemistry, electrical engineering, and computer science. Central to quantum mechanics is Schrödinger's Equation, which explains the behavior of atomic particles and the energy levels of a quantum system. Robert Gilmore's innovative approach to Schrödinger's Equation offers new insight into quantum mechanics at an elementary level. Gilmore presents compact transfer matrix methods for solving quantum problems that can easily be implemented on a personal computer. He shows how to use these methods on a large variety of potentials, both simple and periodic. He shows how to compute bound states, scattering states, and energy bands and describes the relation between bound and scattering states. Chapters on alloys, superlattices, quantum engineering, and solar cells indicate the practical application of the methods discussed. Gilmore's concise and elegant treatment will be of interest to students and professors of introductory and intermediate quantum courses, as well as professionals working in electrical engineering and applied mathematics. |
Inhoudsopgave
Solutions in a Constant Potential | 5 |
Piecewise Constant Potentials | 15 |
Momentum Conservation | 25 |
Units | 33 |
Boundary Conditions | 37 |
A Simple Example | 39 |
Coding and Validation | 43 |
Shape of Barrier | 45 |
Level Splitting | 117 |
Symmetry Breaking | 119 |
Wavefunctions | 123 |
Superpositions Overlaps and Probabilities | 129 |
Symmetry and Wavefunctions | 135 |
Transmission Resonances and Bound States | 143 |
Creation of Bound States | 147 |
Quantum Engineering | 151 |
Asymptotic Behavior | 49 |
Phase Shifts | 53 |
Double Barrier | 59 |
Multiple Barriers | 67 |
Probability Distributions | 69 |
Combining Barriers | 73 |
Quantum Engineering | 79 |
Variations on a Theme | 83 |
Bound States | 89 |
Boundary Conditions | 91 |
A Simple Example | 93 |
Coding and Validation | 95 |
Shape of Potential | 97 |
Dependence on Parameters | 101 |
Relation between Bound and Scattering States | 105 |
Double and Multiple Well Potentials | 113 |
Variations on a Theme | 155 |
The Sine Transform | 159 |
Periodic Potentials | 165 |
Boundary Conditions | 167 |
A Simple Example | 173 |
Coding and Validation | 179 |
Asymptotic Behavior | 183 |
Relation among Boundary Conditions | 187 |
Wavefunctions and Probability Distributions | 193 |
Alloys | 199 |
Superlattices | 203 |
Impurities | 207 |
Quantum Engineering | 213 |
225 | |
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