CHEM 214 Lecture 15: Lecture 15

• School: McGill University
• Department: Chemistry
• Course: CHEM 214
• Professor: Anthony Mittermaier

Document Summary

3d rotation of a diatomic molecule is equivalent to a particle of mass restricted to motion on the surface of a sphere. Spherical coordinates are convenient for describing rotation in 3d. In this case, r is fixed at r = r0. We expect 2 quantum numbers to describe motion on the surface of the sphere. ml related to phi angle in the xy plane while l is related to the angle theta relative to the z- axis. Time-independent because the potential energy does not change with time (continuously 0), and what are the eigenstates of the hamiltonian. Switching the spherical coordinates, holding r constant, and setting. We can separate the wavefunction y into the product of two wavefunctions, one depending on angle theta (respect to z-axis) and one depending only on phi (angle). We need to find equations that satisfy the above equation, and we need to apply boundary conditions.