1. Introduction

• Necessary skills for this course
  • course prerequisites (PHYS 305, PHYS 326)
  • access to the system!
  • familiarity with Linux
  • programming in C/C++
  
  
• "Physics" topics to be covered
  • time-independent Schrodinger equation
    - scaling to dimensionless form
    - finite well
    - harmonic oscillator
  • basis expansion and matrix representation
  • time-dependent Schrodinger equation
    - diffusion
    - wave packets
  • perturbative techniques
  
  
• "Computation" topics to be covered
  • solution of algebraic equations
  • solution of ordinary differential equations
    - initial-value problems (review)
    - boundary-value problems
  • matrix operations
  • numerical integration of functions
  • solution of partial differential equations (diffusive)
  
  
• Numerical Recipes in C, online version
  
  
• Root-finding algorithms

• Exercise 1: Write a short program to calculate the square root of 2 by solving the equation

       z² - 2 = 0

  using the bisection method, starting from guesses z1 = 1, z2 = 2.
  How many iterations are required to reach convergence to 1 part in 10⁶?

• Exercise 2: Repeat Exercise 2, but using the method of false position.

  --> C++ solutions using bisection, false position, the secant method, and Newton's method.
  --> Python solutions using bisection, false position, the secant method, and Newton's method.

• Homework #1