The videos in this course are broadly divided into three parts:
In Part 1, we introduce the basic concepts: Interpretation of the wavefunction, relation to probability, Schrödinger equation, Hermitian operators and inner products. We also discuss wave-packets, time evolution, Ehrenfest theorem and uncertainty.
Part 2 deals with solutions of the Schrödinger equation for one-dimensional potentials. We discuss stationary states and the key problems of a particle moving in: A circle, an infinite well, a finite square well, and a delta-function potential. We examine qualitative properties of the wavefunction. The harmonic oscillator is solved in two ways: Using the differential equation and using creation and annihilation operators. We study barrier penetration and the Ramsaur—Townsend effect.
Part 3 begins with the subject of scattering on the half-line. One can learn in this simpler context the basic concepts needed in 3-dimensional scattering theory: Scattered wave, phaseshifts, time delays, Levinson theorem, and resonances. We then turn to three-dimensional central potential problems. We introduce the angular momentum operators and derive their commutator algebra. The Schrödinger equation is reduced to a radial equation. We discuss the hydrogen atom in detail.