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 2022 at WSU. If you have questions or comments about these notes, please contact Michael McNeil Forbes mailto:mforbes@wsu.edu. For details about other aspects of the course, please contact Nicholas Cerruti mailto:ncerruti@wsu.edu.

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

Instructors: the information presented here at the start of the course documentation is contained in the Docs/index.md file, which you should edit to provide an overview of the course.

One reasonable option might be to replace this by a literal include of the top-level README.md file with the following code:

```{include} ../README.md
``` 

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
• Readings
  • Readings
• References