Cornell University

Department of Physics

Phys 480/680, Astro 690 February 2, 2007

Computational Physics, Spring 2007

Homework Assignment # 2

(Due Wed, February 14 at 5:00pm)

Agenda and readings for the weeks of January 6 and 13:

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.ccmr.cornell.edu/~muchomas/P480.

• Lec 1 01/24 (Tue): Course overview; Introduction to density functional theory.
  Reading: LN ``Overview of quantum mechanics ...'': 1, 2, 3.1-3.2

• Lec 2 01/25 (Thu): Dimensional analysis; overview of numerical integration, mid-point tule, trapezoidal rule.
  Reading: LN: ``Overview of quantum mechanics ...'': 3.3, 5''; ``Numerical Integration ...'' 1-2; NR 4.0-4.2.

• Lec 3 01/31 (Tue): Trapezoidal rule (contd); Richardson extrapolation; Simpson's rule; method of numerical change of variables; Standard form for ODE's
  Reading: LN: ``Numerical Integration ...'' 3-5

• Lec 4 02/02: (Thu): Spherical symmetry in atoms, Poisson's equation; change of variables for infinite domains; simplest general form for ODEs
  Reading: NR 16.0.

• Lab 1 02/02: Digit-shift tests; Rounding errors; care for limiting cases.

• Lec 5 02/07 (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 02/09 (Thu): Kohn-Sham equations; overall plan for solution
  Reading: LN: ``Overview of quantum mechanics ...'': 4,5

• Lec 7 02/14 (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 02/16 (Thu) Secant method; Ridders method
  Reading: NR 9.2

• Lab 2 02/16 (Thu) IEEE arithmetic; 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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