Quantum Wells: Coupled Quantum States and Energy Levels

This lecture discusses quantum wells and their properties, focusing on coupled quantum states and energy levels. The instructor explains the concept of harmonic oscillators and their quantum mechanical behavior, including the energy levels associated with different quantum states. The lecture covers the mathematical formulation of these concepts, including the Schrödinger equation and the role of Hermite polynomials. The instructor illustrates the behavior of particles in potential wells, including the effects of coupling between wells and the formation of molecular states. The discussion includes examples of coupled wells, the transition from single to double wells, and the implications for molecular formation. The lecture also addresses the energy of the vacuum and its physical significance, including the Casimir effect. The instructor emphasizes the importance of understanding these quantum mechanical principles in the context of modern physics and their applications in various fields.