Casting ODEs into Sturm-Liouville form

This lecture covers the process of casting ordinary differential equations (ODEs) into self-adjoint form, specifically focusing on the Sturm-Liouville problem. The instructor explains how to transform a general 2nd order ODE into a Sturm-Liouville form, emphasizing the importance of boundary conditions. The lecture also delves into the Hermite equation as an example, illustrating the steps to convert it into a self-adjoint form and discussing the role of boundary conditions in ensuring self-adjointness. Additionally, the application of Hermite polynomials in the context of the quantum harmonic oscillator is explored, highlighting the relationship between energy eigenstates and Hermite functions.