Thermodynamics, Statistical Physics, and Quantum Mechanics

142

A diatomicrotor confined to aplane would havethreedegrees offreedom,

two translational andone rotational. Hence,

The quantization ofenergy is not apparentsince wehaveassumed

4.44 Diatomic Molecules in Three Dimensions (Stony

Brook, Michigan State)

a) We first transform theexpression of thekineticenergy

where are the Cartesian coordinates of themolecule in theframe
with thec.m. at the origin tosphericalcoordinates:

For the rigid diatom,

We may substitute (S.4.44.2) into (S.4.44.1), obtaining

Using thedefinition of c.m., we may write

SOLUTIONS