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Cornell University
Department of Physics
Phys 480/680, Astro 690 February 11, 2002
Computational Physics, Spring 2002
Homework Assignment # 2
(Due Tuesday, February 19 at 8:40am in Computer Lab.)
Agenda and readings for the week of February 5:
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.
- Lec1 01/22 (Tue): Course overview; Introduction to
density functional theory.
Reading: LN ``Overview of quantum
mechanics ...'': 1, 2, 3.1-3.2, 4 - Lec2 01/29 (Tue): Atomic Units; Formal Density Functional Theory --
Hohenberg-Kohn Theorem, Kohn-Sham Theorem.
Reading: LN
``Overview of quantum mechanics ...'': 5 - Lec3, 01/31 (Thu): Overview of numerical integration; regular
interval methods; midpoint rule, error analysis
Reading: LN: ``Numerical Integration ...'' 1-3; NR 4.0-4.2. - Lec4, 02/05 (Tue): Trapezoidal rule; Richardson Extrapolation;
Simpson's rule; Romberg integration; singular integrals and infinite
domains via change of variables
Reading: LN: ``Numerical Integration ...'' 4-5; NR 4.3-4.4. - Lec5, 02/07 (Thu): Hartree potential in
atoms; Poisson's equation; numerical solution of ordinary differential
equations (ODEs) -- standard form, change of variables, first and
second order methods
Reading: NR 16.0-16.1.
- Lec6, 02/12 (Tue: mini-lecture, 25mins) Runge-Kutta; practical issues;
Overview of ODE solvers.
Reading: NR 16.0-16.1. - Lab1, 02/12 (Tue): Change of variables; Scaling of errors for
, and for periodic functions; IEEE arithmetic; care with
change of variables at limiting cases.
- Lec7, 02/14 (Thu): Schrödinger's equation for
atoms (spherically symmetric solutions); boundary value problems;
standard form for root finding; bisection; secant method; convergence
rates
Reading: NR 17.0-17.1, 9.0-9.1 - Lec8, 02/19 (Tue: mini-lecture, 25mins) Overview of root
finding; Bracketing of roots for Schrödinger's equation.
- Lab2, 02/19 (Tue): Convergence of solution of ODE's; numerical
solutions of Schrödinger's equation.
Note: For the programs in this problem set we face a small
notational difficulty. We have been using the variable n(r) to
represent the number of electrons per unit volume throughout space.
It would make sense then to define an array n[] to hold the values
of the electron density. However, n is so commonly used as an
indexing variable (particularly in Numerical Recipes) that this
is likely to cause difficulties. Thus, we shall use the array rho[]
to represent the electron density n(r).
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Tomas Arias
Mon Feb 11 20:04:44 EST 2002