Cornell University
Department of Physics
Phys 480/680, Astro 690 February 17, 2005
Computational Physics, Spring 2005
Homework Assignment # 3
(Due Thursday, February 24 in lab.)
Agenda and readings for the week of February 12:
Readings marked NR are from Numerical Recipes: The Art of
Scientific Computing, 2
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 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:
- Lec 5 02/08 (Tue): Solution of ODE's in standard form; 1st order,
2nd order, and 4th order methods; correspondences to numeric integration
Reading: NR 16.1.
- Lec 6 02/10 (Thu): Kohn-Sham equations; overall plan for solution
Reading: LN: ``Overview of quantum mechanics ...'': 4
- Lec 7 02/19 (Tue): 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
- Lec 8 02/24 (Thu) Secant/False Position method; Ridders method
Reading: NR 9.2
- Lab 2 02/24 (Thu) Convergence of solution of ODE's; numerical
solutions of Schrödinger's equation.
Preview of coming week:
- Lec 9, 02/22 (Tue) Numerical stability of solution of ODE's,
shooting to a fitting point; Non-spherical states (higher angular
momenta), normalization conventions for atoms.
- Lec 10, 02/24 (Thu): Numerical interpolation; calculation of
total energy in density functional theory.
- Lab 3, 02/24 (Thu): Stability of solutions, effectiveness of root finders; convergence of eigenvalues with N.
Tomas Arias
2005-02-17
