Mathematical Methods: Linear operators on functions
This page covers the contents of the fourth-week lectures, which are all about some common ODEs in physics:
- recognising that many ODEs can be viewed as eigenvalue equations;
- determining the conditions under which they can be viewed as eigenvalue equations involving a Hermitian operator;
- statement of properties of Hermitian operators on infinite-dimensional function spaces;
- examples.
Here are my notes (2-up) and problems. (Notes updated 2/11/12 to correct typo in equ 8.15)
See also sections 21-26 of Fabian Essler’s MT2009 notes and his Problem Set IV.