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fleisch d student s guide schrodinger equation 2020

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Textbook in PDF format Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book. Preface page ix Acknowledgments xi 1 Vectors and Functions 1 1.1 Vector Basics 2 1.2 Dirac Notation 8 1.3 Abstract Vectors and Functions 14 1.4 Complex Numbers, Vectors, and Functions 18 1.5 Orthogonal Functions 22 1.6 Finding Components Using the Inner Product 26 1.7 Problems 30 2 Operators and Eigenfunctions 32 2.1 Operators, Eigenvectors, and Eigenfunctions 32 2.2 Operators in Dirac Notation 37 2.3 Hermitian Operators 43 2.4 Projection Operators 49 2.5 Expectation Values 56 2.6 Problems 60 3 The SchroЁdinger Equation 63 3.1 Origin of the SchroЁdinger Equation 64 3.2 What the SchroЁdinger Equation Means 71 3.3 Time-Independent SchroЁdinger Equation 78 3.4 Three-Dimensional SchroЁdinger Equation 81 3.5 Problems 93 4 Solving the SchroЁdinger Equation 95 4.1 The Born Rule and Copenhagen Interpretation 96 4.2 Quantum States, Wavefunctions, and Operators 98 4.3 Characteristics of Quantum Wavefunctions 102 4.4 Fourier Theory and Quantum Wave Packets 111 4.5 Position and Momentum Wavefunctions and Operators 132 4.6 Problems 144 5 Solutions for Speciﬁc Potentials 146 5.1 Inﬁnite Rectangular Potential Well 147 5.2 Finite Rectangular Potential Well 168 5.3 Harmonic Oscillator 193 5.4 Problems 216 References 218 Index 219

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Fleisch D. A Student's Guide to the Schrodinger Equation 2020.pdf 7.0 MB

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fleisch d student s guide schrodinger equation 2020

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