Quantum Mechanics for Material Science : An Introduction

✍ Scribed by Gianluca Stefanucci

• Publisher: Springer Nature Switzerland
• Year: 2024
• Tongue: English
• Leaves: 241
• Category: Library

✦ Table of Contents

Preface
Contents
1 The Fundamental Concepts of Quantum Mechanics
1.1 The Need to Abandon Classical Physics
1.2 Quantum Solution—The First Five Postulates
1.3 Expectation Value, Variance, and General Considerations
1.4 Observables with Continuum Spectrum and Wavefunction
1.5 Langrangian and Hamiltonian Formalism
1.5.1 Lagrangian Formalism—Euler-Lagrange Equations
1.5.2 Classical Particle in an Electromagnetic Field
1.5.3 Hamiltonian Formalism—Legendre Transform—Hamilton's Equations
1.5.4 Symmetries and Conservation Laws—Poisson Bracket
1.6 The Sixth Postulate
1.7 Generalization of the Fifth Postulate: Schrödinger Equation
1.8 Heisenberg's Uncertainty Principle
1.9 Summary of What We Have Learned So Far
1.10 Exercises
2 Quantum Systems in Finite-Dimensional Hilbert Spaces
2.1 From Operators to Matrices, from Kets to Column Vectors …
2.2 Quantum Systems with Two States—Pauli Matrices
2.3 Exercises
3 Quantum Particle in One Dimension
3.1 Momentum Operator and Hamiltonian
3.1.1 Continuity Equation
3.2 Piecewise Constant Potential
3.3 Piecewise Constant Potential with Dirac Deltas
3.4 Reflection and Transmission Coefficients
3.5 Harmonic Potential
3.5.1 Raising and Lowering Operators
3.5.2 Eigenfunctions and Hermite Polynomials
3.5.3 Coherent States
3.6 Exercises
4 Quantum Particle in Three Dimensions
4.1 Momentum Operator and Hamiltonian
4.2 Virial Theorem
4.3 Separable Hamiltonians
4.4 Quantum Particle in an Electromagnetic Field
4.4.1 Continuity Equation
4.4.2 Static Electromagnetic Field
4.5 Angular Momentum
4.6 Simultaneous Eigenkets of ModifyingAbove upper L With caret squared2 and ModifyingAbove upper L With caret Subscript zz
4.7 Angular Momentum in Polar Coordinates
4.7.1 Spherical Harmonics
4.7.2 Laplacian in Polar Coordinates
4.8 Central Potential
4.9 Hydrogen Atom
4.9.1 Semiclassical Derivation of Hydrogenoid Levels
4.9.2 Radial Functions
4.10 Exercises
5 Spin and Addition of Angular Momenta
5.1 Spin
5.2 Matrix Representation of Spin Operators
5.2.1 Spin 1 divided by 21/2 and Spin 11
5.3 Spin-Orbit Interaction
5.4 Addition of Angular Momenta
5.4.1 Hydrogen Atom with Spin-Orbit Interaction
5.4.2 Heisenberg Hamiltonian for Magnetic Systems
5.5 Exercises
6 Approximation Methods
6.1 Perturbation Theory: Correction to Energy Levels
6.1.1 Correction to Nondegenerate Levels
6.1.2 Correction to Degenerate Levels
6.2 Perturbation Theory: Time Evolution
6.2.1 Fermi Golden Rule
6.2.2 Radiation-Matter Interaction
6.3 Variational Method
6.4 Exercises
Appendix A Dirac Delta: Definition and Properties
Appendix B Levi-Civita Tensor: Definition and Properties
Appendix C Euler's Gamma: Definition and Properties
Index