Quantum Wells: Understanding Potential and Wave Functions

This lecture covers the concept of quantum wells, focusing on potential wells and their significance in quantum mechanics. It begins with an introduction to quantum science and the unique vision it offers. The instructor explains the Schrödinger equation solutions in a vacuum, detailing the harmonic functions and their implications. The discussion progresses to the amplitude and spectral analysis at time t=0, emphasizing the propagation of spectral components. The lecture also addresses phase velocity and group velocity, illustrating their importance in quantum systems. The instructor introduces the concept of total reflection and compares photons to electrons, followed by a detailed examination of potential steps and the continuity of wave functions at interfaces. The phenomenon of tunneling is explored, including its applications in electronic devices and solar cells. The lecture concludes with a discussion on stationary waves and the characteristics of infinite quantum wells, highlighting the discrete energy levels and their relevance in quantum mechanics.