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
3 - Schrödinger Equation; Uncertainty Relations
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 Schroedinger equation for a particle in a potential is introduced and the general properties of its solutions are discussed; the uncertainity relations are derived; the Gram--Schimdt procedure for orthonormalizing a set of independent wave functions is introduced; the time evolution of the expectation values of the position and momentum operatorsfor a particle in a potential and in an electromagnetic field are derived.
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- Chapter
- Information
- Quantum Mechanics through ProblemsWith Complete Solutions, pp. 36 - 60Publisher: Cambridge University PressPrint publication year: 2024