Quantum Mechanics: Free Carrier Concentration and Maxwell Distribution

This lecture covers the fundamental concepts of quantum mechanics related to metals at absolute zero temperature. It begins with calculations of free carrier concentration and average energy of electrons in metals at 0K. The instructor explains the parabolic band structure and density of states, emphasizing the Fermi-Dirac distribution for electron occupancy. The discussion then shifts to the Maxwell distribution, detailing the energy levels of gas atoms and deriving the Maxwell speed distribution for a gas. The lecture also touches on the kinetic theory of gases, illustrating how to determine the average speed and energy of gas molecules. The instructor provides examples and exercises, including the density of carriers in graphene and the concept of phonons in crystalline vibrations. The session concludes with a transition to more advanced topics in quantum computing, setting the stage for future discussions on qubits and quantum harmonic oscillators.