Syllabus of Quantum Mechanics I (PHYS 481/681)


In early 20th century, there were several critical discrepancies between experiments and classical theories, such as famous ultraviolet catastrophe. New theory, instead of patches of classical theories was required. Pioneered by a group of genius scientists, such as Bohr, Plank, Schrodinger, Heisenberg, Einstein, Dirac, etc., quantum mechanics was developed. Quantum mechanics not only fixed the discrepancies, but also successfully predicted new experimental phenomena. Since then, new science and technologies based on quantum mechanics have change people’s life substantially in the past fifty years.

PHYS 481/681 is the first semester course of introduction level quantum mechanics. In this class, we will first introduce old quantum theory for illustrating intuitively new concepts. Then, we will introduce the most important and straightforward description of quantum mechanics, Schrodinger equation, and apply it to solve several ‘stationary’ problems with time-independent potentials. For describing a general system, a mathematically strict formalism is required to separate generic quantum behaviors, which can be applied to all quantum systems, from specific properties of potentials. Finally, we will show how to apply the basic principles of quantum mechanics to describe structures of simple quantum matter, such as hydrogen atom, and calculate interactions between matter and external electric and magnetic fields. To bridge the basic knowledge and cutting-edge research, we will discuss a special topic at the end of each chapter.

PHYS 481/681 is a hybrid course with mixed senior undergraduate students (PHYS 481) and junior graduate students (PHYS 681). The lectures are the same for the two groups of students. Additional problems in homework and tests are added for graduate students.

Textbook

Introduction to Quantum Mechanics, Third Edition. Authors: David J. Griffiths, Darrell F. Schroeter. Publisher: Cambridge University Press; 3 edition (August 16, 2018). ISBN-10: 1107189632. ISBN-13: 978-1107189638.

Course requirements and grade

1. Ten problem sets (40 pts)
2. Three tests (20 pts for each)
3. Contributions in special topics (boost final letter grade by one step)

Prerequisite requirements

1. Calculus
2. Linear algebra
3. Complex number
4. Classical mechanics
5. Electrodynamics (a little bit)
6. Programming (a little bit)

Course outline

  • Old quantum theory
    • Planck blackbody radiation
    • Photoelectric effect
    • Bohr model
  • Schrodinger equation
    • Intuitive "derivation" of Schrodinger equation
    • Explanation of wavefunction
    • Uncertainty principle, Fourier transformation
    • Time-independent Schrodinger equation and stationary states
    • Special topic: matter-wave interferometer
  • Example potentials
    • Free particle
    • Square quantum well
    • Square quantum barrier
    • 1D harmonic oscillator
    • Special topic: rotations and vibrations of diatomic molecules
  • Formalism
    • Hilbert space
    • Eigen-problem
    • Matrix formalism
    • Dirac notation
    • Special topic: quantum information processing
  • Centrifugal field
    • Spherical coordinates
    • Angular momentum
    • Hydrogen atom
    • Special topic: proton radius puzzle
  • Electric and magnetic fields
    • Spin
    • Fine/hyperfine structure
    • Zeeman effect
    • Stark effect
    • Special topic: electron's EDM
  • Identical particles
    • Boson and Fermi particles
    • Introduction of quantum statistics
    • Special topic: Bose-Einstein Condensation and Fermi Degeneracy