Solved Problems in Quantum and Statistical Mechanics (UNITEXT)

Main subject categories: • Quantum mechanics • Statistical mechanics • Problems & solutionsThis textbook is the result of many years of teaching quantum and statistical mechanics, drawing on exercises and exam papers used on courses taught by the authors. The subjects of the exercises have been carefully selected to cover all the material which is most needed by students.Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that students often find difficult, or which are often neglected in other books on the subject. The exercises in this book never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from first principles, rather than by analogy with some previously solved exercise.Part I. Theoretical Background -- Summary of Quantum and Statistical Mechanics -- Part II. Quantum Mechanics - Problems -- Formalism of Quantum Mechanics and One Dimensional Problems -- Angular Momentum and Spin -- Central Force Field -- Perturbation Theory and WKB Method -- Part III. Statistical Mechanics - Problems -- Thermodynamics and Microcanonical Ensemble -- Canonical Ensemble -- Grand Canonical Ensemble -- Kinetic Physics -- Bose-Einstein Gases -- Fermi-Dirac Gases -- Fluctuations and Complements Solved Problems in Quantum and Statistical Mechanics......Page 3 Copyright Page ......Page 4 Preface......Page 5 Table of Contents ......Page 7 Part I Theoretical Background......Page 9 1.1 One Dimensional Schr ̈odinger Equation......Page 11 1.2 One Dimensional Harmonic Oscillator......Page 13 1.3 Variational Method......Page 14 1.4 Angular Momentum......Page 16 1.6 Hydrogen Atom......Page 18 1.7 Solutions of the Three Dimensional Schr ̈odinger Equation......Page 20 1.8 WKB Method......Page 27 1.9 Perturbation Theory......Page 29 1.10 Thermodynamic Potentials......Page 31 1.11 Fundamentals of Ensemble Theory......Page 34 1.11.2 Canonical Ensemble......Page 36 1.11.4 Quantum Statistical Mechanics......Page 37 1.12 Kinetic Approach......Page 38 1.13 Fluctuations......Page 39 1.14 Mathematical Formulae......Page 40 References......Page 44 Part II Quantum Mechanics – Problems......Page 45 2 Formalism of Quantum Mechanicsand One Dimensional Problems......Page 47 3 Angular Momentum and Spin......Page 121 4 Central Force Field......Page 153 5 Perturbation Theory and WKB Method......Page 171 Part III Statistical Mechanics – Problems......Page 199 6 Thermodynamics and Microcanonical Ensemble......Page 201 7 Canonical Ensemble......Page 235 8 Grand Canonical Ensemble......Page 297 9 Kinetic Physics......Page 309 10 Bose-Einstein Gases......Page 323 11 Fermi-Dirac Gases......Page 345 12 Fluctuations and Complements......Page 371 Index......Page 401 This work arises from our teaching this subject during many years. The vast majority of these exercises are the exams we gave to our students in this period. We carefully selected the subjects of the exercises to cover all the material which is most needed℗ and which is treated in the most well known texts on these subjects. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that, from our experience, are found most difficult from the average student. Indeed, several exercises are designed to throw light on℗ aspects of the theory that, for one reason or another, are usually neglected with the result to make the students feel uneasy about them. In fact most students get acquainted just with the more common manipulations,℗ which are illustrated by℗ many examples in textbooks. Our exercises never require extensive calculations℗ but tend to be somewhat unusual℗ and force the solver℗ to think about the problem starting from the principles, rather than by analogy with some previously solved exercise This textbook is the result of many years of teaching quantum and statistical mechanics, drawing on exercises and exam papers used on courses taught by the authors. The subjects of the exercises have been carefully selected to cover all the material which is most needed by students. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that students often find difficult, or which are often neglected in other books on the subject. The exercises in this book never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from first principles, rather than by analogy with some previously solved exercise.