The spectroscopy of diatomic molecules (Herzberg, 1950) serves as a paradigm for the study of larger molecules. In our presentation of the algebraic approach we shall follow a similar route. An important aspect of that presentation is the discussion of the connection to the more familiar geometrical approach. In this chapter we survey those elements of quantum mechanics that will be essential in making the connection. At the same time we also discuss a number of central results from the spectroscopy of diatomic molecules. Topics that receive particular attention include angular momentum operators (with a discussion of spherical tensors and the first appearance of the Wigner-Eckart theorem which is discussed in Appendix B), transition intensities for rovibrational and Raman spectroscopies, the Dunham expansion for energy levels, and the Herman- Wallis expansion for intensities. Two-body quantum mechanical systems are conveniently discussed by transforming to the center-of-mass system. The momentum (differential) operator for the relative motion is . . .p = − iħ∇ . . . . . .(1.1). . . where ∇ is the gradient operator whose square ∇ • ∇ is the Laplacian and, as usual, i2 = − 1 and ħ is Planck’s constant/2π.
Lie algebraic approach to vibrational populations of diatomic molecules in infrared laser fields
