Quantum Mechanics: Particle in a Box

This lecture discusses the quantum mechanics of a particle (either an electron or a helium atom) confined in a cubic box with zero potential energy inside and infinite outside. It covers the Hamiltonian, Schrödinger equation, correspondence principle, operators, separation of the Schrödinger equation, normalization of the wave function, determination of energy levels, and comparison with thermal energy and visible light energy. The lecture concludes with determining the highest occupied energy level for 15 non-interacting electrons at zero temperature, following the Pauli exclusion principle.