Syllabus for Quantum Mechanics
PHYS3109
Current Lecturer
Prof. Jun HU, Email: jhu@suda.edu.cn
Course Time
5th Semester
Lectures: 4 sessions/week, 50min /session, 18 weeks.
Course Description
Quantum mechanics is an advanced course to quantum systems such as atoms, molecules, solids, and so on. With miscellaneous mathematical tools, including calculus up through partial derivative and integration-by-part, linear algebra, and differential equations, quantum mechanics tells the students the general theories and tools to investigate the dynamic properties of particles in the microscopic world. The topics include: Wave function; Time-dependent and independent Schrödinger equations; Quantum theory for Hydrogen atom, Helium atom, and solids; Time-independent perturbation theory, Variational principle, Time-dependent perturbation theory.
Prerequisites
Calculus (00071012/13); Linear Algebra (00071004); Modern Physics (PHYS1027); Methods of Mathematical Physics (PHYS3103)
Textbooks
Introduction to Quantum Mechanics. 2nd ed （影印版）. Griffiths, David J. 机械工业出版社，2006
量子力学导论（第二版），曾谨言，北京出版社，1998
Main contents
Week | Teaching Contents | Sessions | Objectives |
1 | Introduction to the course Schrödinger equation | 2+2 | Introduce the background of the birth of Quantum Mechanics Basic dynamic equation to describe quantum systems Chapter 1.1 |
2 | Wave function Momentum The uncertainty principle | 2+1+1 | Interpret the meaning of wave functions of particles, introduce the normalization of wave functions Mathematic expression of momentum as operator Basic idea of the uncertainty principle Chapter 1.2-1.4, Chapter 1.5, Chapter 1.6 |
3 | Stationary states Infinite square well | 2+2 | Introduce the time-independent Schrödinger equation and basic characters of the corresponding solutions Application of the time-independent Schrödinger equation to infinite square well Chapter 2.1, Chapter 2.2 |
4 | Finite square well | 4 | Apply the time-independent Schrödinger equation to finite square well, the difference between results from quantum and classical theories Chapter 2.6 |
5 | Delta-function potential Free particle | 2+2 | Apply the time-independent Schrödinger equation to delta-function potentials Wave functions for free particles Chapter 2.5, Chapter 2.4 |
6 | Harmonic oscillator | 4 | Apply the time-independent Schrödinger equation to parabolic potential, introduce ladder operators Chapter 2.3 |
7 | Hilbert space Dirac notation Observables Eigenfunctions of a Hermitian operator | 1+1+1+1 | Introduce Hilbert space Introduce Dirac notation Operators for observables in quantum mechanics Discuss properties of eigenfunctions of a Hermitian operator Chapter 3.1, Chapter 3.6, Chapter 3.2, Chapter 3.3 |
8 | Generalized statistical interpretation The uncertainty principle Schrödinger equation in spherical coordinates | 1+1+2 | Generalize the statistical interpretation of wave functions Restrict proof of the uncertainty principle Solutions to the angular equation and the radial equation Chapter 3.4, Chapter 3.5, Chapter 4.1 |
9 | The Hydrogen atom | 4 | Solve to the radial equation for Hydrogen atom, and discuss the eigenvalues and eigenfunctions Chapter 4.2 |
10 | Midterm exam Angular momentum | 2+2 | Midterm exam for Chapter 1~3 Get eigenvalues and eigenfunctions of angular momentum with the ladder-operator method Chapter 4.3 |
11 | Spin | 4 | Eigenvalues and eigenfunctions for spin 1/2 Electron in magnetic field Addition of angular momenta Chapter 4.4 |
12 | Two-particle systems Atoms
| 2+2 | Introduce the concepts of identical particles, the Bosons and Fermions, and exchange forces Solutions of the Schrödinger equation for Helium atom, introduce the general electronic configurations of atoms in the periodic table Chapter 5.1, Chapter 5.2 |
13 | Quantum statistical mechanics | 4 | Generalize the Statistical Mechanics to quantum systems, with the characteristics of Bosons and Fermions Chapter 5.4 |
14 | Nondegenerate perturbation theory Degenerate perturbation theory | 2+2 | General theory, first- and second-order corrections to energies, first-order correction to eigenfunctions General perturbation theory for degenerate states Chapter 6.1, Chapter 6.2 |
15 | Fine structure of Hydrogen Variational principle | 2+2 | Apply perturbation theory to hydrogen atom Chapter 6.3, Chapter 7.1 |
16 | Ground state of Helium Time-dependent perturbation theory | 2+2 | Apply the variational principle to get the ground state energy of helium atom General theory for time-dependent perturbation Chapter 7.2, Chapter 9.1 |
17 | Emission and absorption of radiation Review of the whole course | 2+2 | Quantum theory of photon emission and absorption General Review and Preparation for final exams Chapter 9.2 |
Marking Scheme:
Activities | Homework | Attendance | Midterm | Final exam |
Percentages | 10% | 10% | 20% | 60% |
