Quantum Mechanics: Spatial Interference and Coupling

This lecture focuses on exercises related to quantum mechanics, specifically addressing spatial interference and coupling between oscillators. The instructor begins by emphasizing the importance of attempting exercises independently before discussing solutions. The first exercise introduces two coupled oscillators and explores the concept of overlap between their modes. The instructor explains how to find the Hamiltonian by determining projectors and using eigenvalues. The discussion progresses to the interpretation of symmetric and antisymmetric modes, their energies, and how coupling affects the system. The second exercise involves time evolution of a wave function in a coupled system, utilizing propagators and analyzing probabilities of finding particles in specific states. The instructor highlights the significance of understanding quantum states and their evolution, particularly in the context of quantum information and cryptography. The lecture concludes with a discussion on the implications of measurement and observation in quantum mechanics, emphasizing the role of entanglement and the observer's influence on quantum systems.