HW # 2. Chem 1410, Spring 2001

Assigned Tuesday 16; Due Thursday Jan 25.

- Using the 2-dimensional particle-in-the-box problem accessible via the class web page, plot the wavefunctions of the (1,1), (1,2), (2,1), (2,2), and (3,2) solutions where (n,m) refer to the two quantum numbers. Sketch the solutions, imagining that you are looking down from the "top" of the box toward the (x,y) plane.
- Run some calculations with the tunneling program also accessible from the web page. Sketch how the wavefunction changes in the classically forbidden region when you double the mass of the particle. How does the wavefunction change when you double the width of the barrier? When you choose vary the energy?
- Search the WWW for a program that solves for the energy levels of an electron in a spherical box. If you find such a program and are able to execute it, use it to study the three lowest energy solutions of this system. Describe the wavefunctions. If you cannot locate a program that solves this problem, search instead for a program that for solving for the energy levels of a particle in a finite box problem. Using this computer program, determine whether this problem has at least one bound level regardless of the width and depth of the potential.
- Using Mathcad (you can substitute Maple or Mathematica) evaluate symbolically the integral of exp(-x
^{2}) with the integration limits of 0 and infinity. Also show that the functions sin(p x/L) and sin(2p x/L) are orthogonal on the range (0,L).