1 Raison d’être 1 1.1 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schrödinger Operator with Periodic Potential . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Direct Integral Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Bloch Periodic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Previously published material has been reprinted with permission from the copyright holder. All illustrations unless otherwise specified are made by the author. Le coeur a ses raisons que la raison ne connaît point. v ABSTRACT Background: