上課地點：化121教室
Chapter 1 Linear Algebra

1.1. Basic Concepts

1.2. Matrix Multiplication

1.3. Linear Systems of Equations

1.4. Linear Independence and Rank

1.5. Solutions of Linear Systems

1.6. Determinants

1.7. Inverse of an n (8465) n Square Matrix

Chapter 2 Group Theory

2.1. Symmetry

2.2. Matrix Representation of Symmetry Operations

2.3. Product of Symmetry Operations

2.4. Definition of Group

2.5. Irreducible Representation and the Character Table

2.6. Direct Product

2.7. Application Examples of the Character Table

Chapter 3 Matrix Eigenvalue Problems

3.1. Eigenvalues and Eigenvectors

3.2. Symmetric, Skew-Symmetric and Orthogonal Matrices

3.3. Complex Matrices: Hermitian, Skew-Hermitian, Unitary

3.4. Operator Representation

3.5. Similarity of Matrices and Diagonalization

3.6. Kets, Bras, and Operators

3.7. Measurements and the Uncertainty Principle

Chapter 4 Theory of Angular Momentum

Ref: J. J. Sakurai, “Modern Quantum Mechanics”, Chapter 3

4.1. Rotations

4.2. Commutation Relations

4.3. Euler Rotations

4.4. Eigenvalues and Eigenvectors of Angular Momentum

4.5. Addition of Angular Momenta

Chapter 5 Fourier Transformation

Ref: - Textbook, Chapter 10

- J. F. James, “A student’s guide to Fourier transforms: with applications in physics and engineering”

- R. N. Bracewell, “The Fourier Transform and Its Applications,”

5.1. Fourier Series

5.2. Fourier transforms

5.3. Discrete Fourier Transformation

5.4. Useful Functions

5.5. Properties of Fourier Transformation

5.6. NMR Spectrum

5.7. Interference Spectrometry