Quantized Rotational Motion in a Plane

Abstract

The angular momentum for the simplified case of a particle rotating in a fixed plane is treated. The ‘perimeter model’ is the analogue of the one-dimensional particle in a box (PiaB), with the particle moving on a circle with fixed radius. This requires cyclic – or periodic – boundary conditions. It is shown that the quantum perimeter model results can be obtained by re-interpreting the coordinate of the linear PiaB and by considering the periodic boundary conditions. The eigenvalue pattern leads to a 4n+2 Huckel rule. Next, the chapter discusses hindered rotations, such as the rotation of a methyl group around a C-C bond. The solutions to the hindered rotation problem combine features of the harmonic oscillator at low energies, with features of the perimeter model at high energies.