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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. Cover Half-title Series information Title page Copyright information About this book Contents Preface Acknowledgments 1 Vectors and Functions 1.1 Vector Basics 1.2 Dirac Notation 1.3 Abstract Vectors and Functions 1.4 Complex Numbers, Vectors, and Functions 1.5 Orthogonal Functions 1.6 Finding Components Using the Inner Product 1.7 Problems 2 Operators and Eigenfunctions 2.1 Operators, Eigenvectors, and Eigenfunctions 2.2 Operators in Dirac Notation 2.3 Hermitian Operators 2.4 Projection Operators 2.5 Expectation Values 2.6 Problems 3 The Schrödinger Equation 3.1 Origin of the Schrödinger Equation 3.2 What the Schrödinger Equation Means 3.3 Time-Independent Schrödinger Equation 3.4 Three-Dimensional Schrödinger Equation 3.5 Problems 4 Solving the Schrödinger Equation 4.1 The Born Rule and Copenhagen Interpretation 4.2 Quantum States, Wavefunctions, and Operators 4.3 Characteristics of Quantum Wavefunctions 4.4 Fourier Theory and Quantum Wave Packets 4.5 Position and Momentum Wavefunctions and Operators 4.6 Problems 5 Solutions for Specific Potentials 5.1 Infinite Rectangular Potential Well 5.2 Finite Rectangular Potential Well 5.3 Harmonic Oscillator 5.4 Problems References Index 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 Schrodinger 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 Schrodinger 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. Retaining the successful approach used in Fleisch's other Student's Guides, this accessible resource provides plain language explanations of the key concepts and techniques underlying the Schroedinger equation in quantum mechanics. A companion website hosts additional resources including videos and quizzes to further develop students understanding. Retaining the successful approach used in Fleisch's other Student's Guides, this accessible resource provides plain language explanations of the key concepts and techniques underlying the Schrödinger equation in quantum mechanics. A companion website hosts additional resources including videos and quizzes to further develop students understanding. A Clear Guide To The Key Concepts And Mathematical Techniques Underlying The Schrödinger Equation, Including Homework Problems And Fully Worked Solutions.