Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 The Failure of Classical Physics
- 2 Wave–Particle Duality andWave Mechanics
- 3 Schrödinger Equation; Uncertainty Relations
- 4 The One-Dimensional Schrödinger Equation; Bound States
- 5 Scattering in One Dimension
- 6 Mathematical Formulation of Quantum Mechanics
- 7 Physical Interpretation: Postulates of Quantum Mechanics
- 8 The Harmonic Oscillator
- 9 Particle in a Central Potential; Orbital Angular Momentum
- 10 Bound States in a Central Potential: Applications
- 11 Angular Momentum: General Properties
- 12 Spin; Charged Particle in an Electromagnetic Field
- 13 Addition of Angular Momenta
- 14 Approximation Methods
- 15 Scattering by a Potential
- 16 Symmetry Transformations of States and Operators
- 17 Rotation Matrices and the Wigner–Eckart Theorem; Fine and Hyperfine Structure of Energy Levels in Hydrogen-Like Atoms
- 18 Time-Dependent Perturbation Theory
- 19 Systems of Identical Particles
- Bibliography
- Index
6 - Mathematical Formulation of Quantum Mechanics
Published online by Cambridge University Press: 05 December 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 The Failure of Classical Physics
- 2 Wave–Particle Duality andWave Mechanics
- 3 Schrödinger Equation; Uncertainty Relations
- 4 The One-Dimensional Schrödinger Equation; Bound States
- 5 Scattering in One Dimension
- 6 Mathematical Formulation of Quantum Mechanics
- 7 Physical Interpretation: Postulates of Quantum Mechanics
- 8 The Harmonic Oscillator
- 9 Particle in a Central Potential; Orbital Angular Momentum
- 10 Bound States in a Central Potential: Applications
- 11 Angular Momentum: General Properties
- 12 Spin; Charged Particle in an Electromagnetic Field
- 13 Addition of Angular Momenta
- 14 Approximation Methods
- 15 Scattering by a Potential
- 16 Symmetry Transformations of States and Operators
- 17 Rotation Matrices and the Wigner–Eckart Theorem; Fine and Hyperfine Structure of Energy Levels in Hydrogen-Like Atoms
- 18 Time-Dependent Perturbation Theory
- 19 Systems of Identical Particles
- Bibliography
- Index
Summary
The state space of a quantum system is defined; kets and bras are introduced, and their inner and outer products are defined; adjoint, hermitian , and unitary operators are introduced; representations of states and operators on discrete and/or continuous bases are discussed; the properties of commuting hermitian operators are examined; tensor products are defined.
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- Quantum Mechanics through ProblemsWith Complete Solutions, pp. 155 - 191Publisher: Cambridge University PressPrint publication year: 2024