<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. ABSTRACTING & INDEXING Quantum Mechanics I is covered by the following services: <UL> <LI>EBSCO Discovery Service </LI> <LI>J-Gate </LI> <LI>Naviga (Softweco) </LI> <LI>Primo Central (ExLibris) </LI> <LI>ReadCube </LI> <LI>Summon (ProQuest) </LI> <LI>TDOne (TDNet) </LI></UL></DIV>

"This book is excellent for learning the basics of Quantum Mechanics by self-study. It can also be a good supplement for an introductory undergraduate course in the subject." Amitava Raychaudhuri in: zbMATH 1408.81001

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

A Problem Text

Quantum Mechanics I

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

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

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"}}

Chapter 10. The Simple Harmonic Oscillator

Chapter 10. The Simple Harmonic Oscillator

{"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.

Index

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

Chapter

Book Details

Quantum Mechanics I

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

Published Online on: 31 Aug 2018

Book Details

PDF Preview

Table of Contents

Frontmatter

Dedication

Preface

Prologue

Table of Contents

Chapter 1. Discrete Systems I

Chapter 2. Probability, Statistics, and Stationary States

Chapter 3. Discrete Systems II

Chapter 4. Continuous Systems I

Chapter 5. Continuous Systems II

Chapter 6. Ehrenfest, Heisenberg, and Gauss

Chapter 7. The Free Particle

Chapter 8. The Infinite Square Well

Chapter 9. Scattering in One Dimension

Chapter 10. The Simple Harmonic Oscillator

Chapter 11. The Finite Square Well

Chapter 12. Orbital Angular Momentum

Chapter 13. The Hydrogen Atom

Appendix A. Arithmetic with Complex Numbers

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

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

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

Index

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