Quantum Mechanics: Harmonic Oscillator and Molecular Interactions

This lecture covers the fundamental concepts of the harmonic oscillator in quantum mechanics, starting from classical mechanics principles. The instructor discusses the interaction of two masses, M1 and M2, connected by a spring, and how this can represent two atoms interacting through electrostatic forces. The total energy of the system is analyzed, including the center of mass motion and relative motion. The lecture transitions into quantum mechanics, deriving the Hamiltonian for the harmonic oscillator and solving the time-independent Schrödinger equation. The energy levels and wave functions are explored, highlighting the differences between quantum and classical mechanics. The concept of zero-point energy is introduced, emphasizing that even at absolute zero, the system retains energy. The instructor also discusses the significance of the harmonic oscillator in understanding molecular vibrations and the implications for chemical bonding. The lecture concludes with applications of these concepts in spectroscopy and the measurement of molecular properties through light absorption.