For many years, Professor Marmorino has been developing and using Mathematica to create tutorial programs that allow students to explore quantum mechanical phenomena in our upper-level CHEM-C 362 Physical Chemistry of Molecules course. There students explore the two-dimensional particle in a box, particle on a ring, the Bohr correspondence principle with the harmonic oscillator, the action of linear operators on functions, the non-linear variational method for a particle in one and two wells, the linear variational method for a hydrogenic atom, the bonding and anti-bonding molecular orbitals for the hydrogen molecular ion, hybrid orbitals, and the Hückel molecular orbital method. The image below shows the four molecular orbitals of cyclobutadiene generated as just part of the Hückel molecular orbital program.
Most recently, Marmorino has developed a new program to illustrate the time dependence of stationary states, and binary linear combinations of these, for a particle in a box. Without the time dependence of wavefunction, it is hard to appreciate the wavefunction's "waviness" that is familiar to us in our classical experience of moving ocean waves. The program also allows one to investigate the transition from one stationary state to another and how this depends on the system's transition dipole moment. This program is available to the public through the Chemical Educator, which also published Marmorino's corresponding article on how various aspects of time dependence can be illustrated and investigated using the program.
