Eastham M.S.P. The Spectral Theory of Periodic Differential Equations

Scittish Academic Press, 1973. — 136 p.
The second-order linear ordinary differential equation with real periodic coefficients, commonly known as Hill's equation, has been investigated by many mathematicians in recent years. An account of much of this theory, in part summarized, is given in the book by Magnus and Winkler. Further results relating to eigenfunction theory are given by Titchmarsh. It seemed to me that, in addition to the material in these two references, there remained among the papers in the journals a body of results relating to eigenvalue and spectral theory that had yet to be brought together in the form of a book. One of my two aims in writing this book was, therefore, to present a connected account of such results. My second aim concerned the second-order partial differential equation known as the Schrodinger equation, in which the potential function is periodic in N dimensions. This equation arises in solid state physics and the theory of metals in connexion with the quantum mechanics of crystals.
M.S.P. Eastham