ABSTRACT
This chapter discusses the concept of a Sturm-Liouville problem. It shows the reader how to solve a Sturmp-Liouville problem. The chapter deals with eigenvalues and eigenfunctions, orthogonal expansions, singular Sturm-Liouville, and separation of variables. Sturm-Liouville problems arise in many parts of mathematical physics—both elementary and advanced. One of these is quantum mechanics. The chapter examines the conditions under which such a boundary value problem has a nontrivial solution. It looks at more basic applications to classical physics, focusing on the most classical application to mechanics, the vibrating string. The chapter examines how the study of matter on a very small scale can be effected.
