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Quantum Mechanics I

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Quantum mechanics; quantum physics; quantum theory; mathematical physics; problem text

<DIV align=justify> The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology. Applications of the postulates are presented initially using arguments from linear algebra appropriate to discrete systems with low-dimensional vectors and matrix operators, introducing orthogonality, orthonormality, Hermiticity, eigenvectors, eigenvalues, probability, expectation value, and degeneracy. These arguments blend into infinite-dimensional vectors and operators, and calculus-based arguments for continuous systems where delta functions, theta functions, and Fourier transforms are initially discussed. Dirac notation is fully developed within these first five chapters. Chapter six discusses Ehrenfest’s theorem, the Heisenberg uncertainty relations, and Gaussian wave functions and wave packets. Increasingly sophisticated potential energy functions are then treated to include the free particle, the infinite square well, the one-dimensional scattering state, the simple harmonic oscillator, the finite square well, orbital angular momentum, and the hydrogen atom. Ladder operators are featured in the developments of the simple harmonic oscillator and orbital angular momentum. The diversity of narratives and detailed solutions intend to allow students to solve comparable unsolved exercises at the end of each chapter/section whether used as a primary text, a supplementary text, or for self-study.

A Problem Text

Chapter 10. The Simple Harmonic Oscillator

Chapter 10. The Simple Harmonic Oscillator

Frontmatter

{"title":{"xml:lang":"en","content":"Frontmatter"}}

Dedication

{"title":{"xml:lang":"en","content":"Dedication"}}

Preface

{"title":{"xml:lang":"en","content":"Preface"}}

Prologue

{"title":{"xml:lang":"en","content":"Prologue"}}

Table of Contents

{"title":{"xml:lang":"en","content":"Table of Contents"}}

Chapter 1. Discrete Systems I

The Postulates and Initial Essentials

Chapter 2. Probability, Statistics, and Stationary States

Chapter 2. Probability, Statistics, and Stationary States

{"title":{"xml:lang":"en","content":"Chapter 2. Probability, Statistics, and Stationary States"}}

Chapter 3. Discrete Systems II

A Complete Set of Commuting Observables

Chapter 4. Continuous Systems I

{"title":{"xml:lang":"en","content":"Chapter 4. Continuous Systems I"}}

Chapter 5. Continuous Systems II

{"title":{"xml:lang":"en","content":"Chapter 5. Continuous Systems II"}}

Chapter 6. Ehrenfest, Heisenberg, and Gauss

Chapter 6. Ehrenfest, Heisenberg, and Gauss

{"title":{"xml:lang":"en","content":"Chapter 6. Ehrenfest, Heisenberg, and Gauss"}}

Chapter 7. The Free Particle

{"title":{"xml:lang":"en","content":"Chapter 7. The Free Particle"}}

Chapter 8. The Infinite Square Well

{"title":{"xml:lang":"en","content":"Chapter 8. The Infinite Square Well"}}

Chapter 9. Scattering in One Dimension

{"title":{"xml:lang":"en","content":"Chapter 9. Scattering in One Dimension"}}

{"title":{"xml:lang":"en","content":"Chapter 10. The Simple Harmonic Oscillator"}}

Chapter 11. The Finite Square Well

{"title":{"xml:lang":"en","content":"Chapter 11. The Finite Square Well"}}

Chapter 12. Orbital Angular Momentum

{"title":{"xml:lang":"en","content":"Chapter 12. Orbital Angular Momentum"}}

Chapter 13. The Hydrogen Atom

{"title":{"xml:lang":"en","content":"Chapter 13. The Hydrogen Atom"}}

Appendix A. Arithmetic with Complex Numbers

Appendix A. Arithmetic with Complex Numbers

{"title":{"xml:lang":"en","content":"Appendix A. Arithmetic with Complex Numbers"}}

Appendix B. Linear Independence and the Gram-Schmidt Orthonormalization Process

Appendix B. Linear Independence and the Gram-Schmidt Orthonormalization Process

Appendix C. The Gaussian Wave Packet Centered at k = k0.

Appendix C. The Gaussian Wave Packet Centered at k = k.

Appendix D. Second Derivative of the Associated Laguerre Function Used for Hydrogen

Appendix D. Second Derivative of the Associated Laguerre Function Used for Hydrogen

Index

{"title":{"xml:lang":"en","content":"Index"}}

<DIV align=left> David DeBruyne and Larry Sorensen </DIV>

 The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum mechanics. Significantly detailed solutions to traditionally posed problems dominate. Theory and rationale are addressed in prescript and postscript narratives and/or within the solved problems to guide students; and clarify vocabulary, symbology, and terminology.

 The goal of Quantum Mechanics I, A Problem Text, is to enable students to solve problems appropriate to their first course in quantum...

Chapter 10. The Simple Harmonic Oscillator - Quantum...

Title

Chapter 10. The Simple Harmonic Oscillator

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