Lecture · MIT
Lecture 9: Operator Methods for the Harmonic Oscillator
MIT OpenCourseWare
Allan Adams's lecture from MIT's 8.04 Quantum Physics I (Spring 2013) solves the oscillator a second way, with raising and lowering operators instead of a differential equation. The algebra runs ahead of this course, but watch how a single commutation rule between the two operators generates the entire evenly spaced ladder, a structure Adams promises you will meet again all the way up to quantum field theory.