Cornell University

Department of Physics

Phys 480/680, Astro 690 February 12, 2004

Computational Physics, Spring 2004

Homework Assignment # 2

(Due Thu, February 19 during check-off times in Rock B3.)

Agenda and readings for the week of February 5:

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.

• Lec1 01/27 (Tue): Course overview; Introduction to density functional theory.
  Reading: LN ``Overview of quantum mechanics ...'': 1, 2, 3.1-3.2

• Lec2 01/29 (Thu): Importance of simplication, simplifications to density-functional theory (dimensional analysis), overview of numerical integration.
  Reading: NR 4.0-4.2.

• Lec3 02/03 (Tue): Class cancelled

• Lec4 02/04 (Thu): Trapezoidal rule; Richardson extrapolation; Simpson's rule; method of numerical change of variables
  Reading: LN: ``Numerical Integration ...'' 1-5

• Lec5 02/10 (Tue): Change of variables for infinite domains; Spherical symmetry in atoms; Poisson's equation; Standard form for ODE's
  Reading: NR 16.0-16.1.

• Lec6 02/12 (Thu): Solution of ODE's in standard form; 1st order, 2nd order, and 4th order methods; correspondences to numeric integration
  

• Lab1 02/13: Digit-shift tests; errors for $\int_0^1 \sqrt{x} \, dx$ and integrals of periodic functions, IEEE arithmetic, care for limiting cases

• Lec7, 02/17 (Tue): Kohn-Sham equations.
  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; secant method; convergence rates
  Reading: NR 17.0-17.1, 9.0-9.1

• Lab2, 02/20 (Fri): 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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