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
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
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.
Keywords
Information
- Type
- Chapter
- Information
- Quantum Mechanics through ProblemsWith Complete Solutions, pp. 155 - 191Publisher: Cambridge University PressPrint publication year: 2024
Accessibility standard: Unknown
Why this information is here
This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.Accessibility Information
Accessibility compliance for the PDF of this chapter is currently unknown
and may be updated in the future.
You have
Access