Quantized Vibrational Motion

The harmonic oscillator of chapter 2 is visited again, now in its quantum theoretical version. The solution of the Schrodinger equation (SE) is shown step-by step, as it features steps that are very similar to those used in solving the equations for the angular momentum and hydrogen-like orbitals in later chapters. The Morse oscillator has a potential function that is much more representative of the vibrations of atoms in molecules as the harmonic potential. The solutions of the harmonic and Morse oscillator are compared. It is then shown how nuclear vibrations in poly-atomic molecules are treated at the harmonic level. This requires the separation of internal degrees of freedom from the overall translation and rotation of a molecule, leading to the normal modes. The chapter also discusses basic aspects of vibrational spectroscopy and the selection rules of infrared and Raman vibrational spectroscopy.