Physics 552 - Quantum Theory III

These are incomplete notes for some guest lectures about the renormalization group for Physics 552, Quantum Theory III offered in the Spring of 2026 at WSU. If you have questions or comments about these notes, please contact Michael McNeil Forbes mforbes@wsu.edu. For details about other aspects of the course, please contact Qingze Guan qingze.guan@wsu.edu.

Phys 552 - Quantum Theory III

Welcome to Phys 552 - Quantum Theory III! This is the main documentation page for the course. For more class information, please see the Syllabus.

This website, hosted on Read The Docs, will be used to collect and display additional information about the course, including:

• Syllabus

• Resources, Readings, and References

and various class notes. These should also be available through the navigation menu (which might hidden if your display is not sufficiently wide).

These documents are built using JupyterBook (see JupyterBook Demonstration) and include all of the source code needed to generate the figure, plots etc. For example, to see how a figure was made, look in the preceding code cell. The complete source code for this documentation is available at wsu-courses/physics-552-quantum-iii.

Contents:

• Renormalization Group Techniques
  • The Essence
  • Random Walks
  • How to Renormalize the Schrödinger Equation
  • Ising Model
  • Philosophy
• Renormalizing Random Walks
  • Gaussian Random Walks: A Fixed Point
    • Examples
  • Random Walks: Universality
    • Symmetries
    • Universality
  • Biased Random Walk
    • Basins of Attraction
  • Extensions: Other Universality Classes
• How to Renormalize The Schrödinger Equation
  • How to Solve the Schrödinger Equation
    • Radial Equation
  • The Essence
  • Numerical Approach
  • Figure 1

Appendices:

• How to Solve the (Radial) Schrödinger Equation
  • To Do
  • Simple Solution: Shooting
  • Asymptotic Behaviour
  • A Solution: Integrate Backwards
  • How to Solve the Schrödinger Equation (Old)
    • Radial Equation
    • DVR Basis for the Radial Equation
    • Demonstration
• Chaos and Feigenbaum’s Constant
  • Bifurcation Diagrams
  • Fixed Points
    • Period 1
    • Period 2
    • Period 3 Implies Chaos
  • Exact solution for \(r=4\): Angle doubling on the unit circle
  • Feigenbaum Constants
• Resources, Readings, and References
  • Readings
• References
  • Linear Algebra