These are preliminary lectures that cover topics that you should be comfortable in before you start the Advanced QM course. Most of these things have already been covered in earlier courses.
This is a lecture that takes a look at how to solve the Schrodinger equation for the Simple Harmonic Oscillator. I explore the motivation behind the different mathematical manipulations that are carried out in the process. In particular, I try to explain how the singularities of a differential equation dictate different choices that you make when trying to solve it.
I assume that you are acquainted with the basic notion of singularities of a function (from elementary complex analysis), as well as the related notion of singularities of an ordinary differential equation.
