Quantum Physics I

This lecture delves into the quantum harmonic oscillator, emphasizing the importance of creation and annihilation operators in diagonalizing the Hamiltonian. The discussion covers eigenstates, wave functions, and the quantization of energy levels. The instructor demonstrates the creation and destruction of excitations, highlighting the orthogonality of excited states. The lecture explores the Hermitian polynomials, showcasing their nodal properties and their role in quantum mechanics. The Hermitian theorem is introduced, connecting quantum and classical physics by showing how average values evolve similarly in both realms. The lecture concludes with a demonstration of Hermit's theorem, illustrating how the dynamics of quantum systems mirror classical systems at the mean level.