Cornell University

Department of Physics

Phys 480/680, Astro 690 February 20, 2004

Computational Physics, Spring 2002

Homework Assignment # 3

(Due Thursday, February 26 during checkoff hours.)

Agenda and readings for the week of February 12:

Readings marked NR are from Numerical Recipes: The Art of Scientific Computing, 2$^{\mathrm nd}$ edition (in C). Readings marked LN are from the course lecture notes to be found at http://www.muchomas.lassp.cornell.edu/P480.
Goal: This problem set develops a fully automated solver which finds all of the energy states for any specified external potential ``V[]'' to high precision.

Readings marked NR are from Numerical Recipes: The Art of Scientific Computing, 2$^{\mathrm nd}$ edition (in C). Readings marked LN are from the course lecture notes to be found at http://www.muchomas.lassp.cornell.edu/P480.

Recap of last week:

• Lec7, 02/17 (Tue): Derivation of Kohn-Sham equations, and overview of plan of attack for atoms
  Reading: LN: ``Overview of quantum mechanics ...'': 4,5

• Lec8, 02/19 (Thu): Schrödinger's equation for atoms (spherically symmetric solutions); boundary value problems; standard form for root finding; bisection; convergence rates
  Reading: NR 17.0-17.1, 9.0-9.1

• Lab2, 02/20 (Fri): IEEE arithmetic; convergence of solution of ODE's; numerical solutions of Schrödinger's equation.

Preview of coming week:

• Lec9, 02/24 (Tue) Secant method; Ridders method; bracketing of roots for Schrödinger's equation
  Reading: NR 9.2

• Lec10, 02/26 (Thu): Interpolation; shooting to a fitting point; normalization conventions for atoms; Non-spherical states (higher angular momenta)
  Reading: NR 3.0-3.2

• Lab3, 02/27 (Fri): Stability of solutions, effectiveness of root finders; convergence of eigenvalues with N.

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