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80 pages

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English

This book covers the basic principles of quantum mechanics along with key introductory topics.

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Description

Content

- A brief historical note on the origin of quantum mechanics
- The insuffiency of classical physics

- The insuffiency of classical physics
- Fundamental principles and theorems in quantum mechanics
- Describing particles as waves
- The postulates of quantum mechanics
- Eigenvalues and eigenfunctions
- Expansion via eigenfunctions
- Probability current and density
- Simultaneous eigenfunctions
- Time-evolution of expectation values
- The Ehrenfest theorem
- Heisenberg’s uncertainty principle

- Describing particles as waves
- Solving the Schrödinger equation: bound states and scattering
- Stationary states
- Time-energy uncertainty: what it really means
- Collapse of the wavefunction and superpositions
- Wavefunction properties
- Particle in a potential well
- The δ-function potential

- Stationary states
- Quantum harmonic oscillator and scattering
- Harmonic oscillator
- Quantum mechanical scattering

- Harmonic oscillator
- Quantum mechanics beyond 1D
- Particle in a box
- Harmonic oscillator
- 2D potentials with polar coordinates

- Particle in a box
- Quantization of spin and other angular momenta
- Orbital angular momentum
- Central potentials and application to the Coulomb potential
- Generalized angular momentum operators
- Quantum spin

- Orbital angular momentum
- Quantum statistics and exchange forces
- Symmetry of the wavefunction
- The Pauli exclusion principle and its range
- Exchange forces due to the Pauli principle

- Symmetry of the wavefunction
- Periodic potentials and application to solids
- Bloch functions
- Band structure and the Kronig-Penney model

- Bloch functions

The aim of this book is to provide the reader with an introduction to quantum mechanics, a physical theory which serves as the foundation for some of the most central areas of physics ranging from condensed matter physics to astrophysics. The basic principles of quantum mechanics are explained along with important belonging theorems. We then proceed to discuss arguably the most central equation in quantum mechanics in detail, namely the Schrödinger equation, and how this may be solved and physically interpreted for various systems. A quantum treatment of particle scattering and the harmonic oscillator model is presented. The book covers how to deal with quantum mechanics in 3D systems and explains how quantum statistics and the Pauli principle give rise to exchange forces. Exchange forces have dramatic consequences experimentally and lie at the heart of phenomena such as ferromagnetism in materials. Finally, we apply quantum mechanics to the treatment of angular momentum operators, such as the electron spin, and also discuss how it may be applied to describe energy bands in solids.

J.L. holds since 2013 a position as Professor of Physics at the Norwegian University of Science and Technology. His research is focused on theoretical quantum condensed matter physics and he has received several prizes for his Ph.D work on the interplay between superconductivity and magnetism. He has also received the American Physical Society ”Outstanding Referee” award, selected among over 60.000 active referees. In teaching courses such as Classical Mechanics and Particle Physics for both undergraduate and graduate students, he has invariably received high scores from the students for his pedagogical qualities and lectures. His webpage is found here.