ABSTRACT
This chapter shows that the laws of conventional optics are a consequence of the linearity of Maxwell's equations, which permit the superposition of different waves. Experiments on electron diffraction show that the interference phenomena associated with these "matter waves" obey the familiar laws of physical optics. The chapter provides the linearly independent solutions of the Schrodinger equation form a complete set of functions. The form of the Schrodinger equation is intimately connected with the requirement of gauge invariance. In classical transformation theory, the Hamiltonian H is the generator of displacements in time. In classical mechanics the total linear and angular momenta are constants of the motion if the Hamiltonian is invariant under translations and rotations, respectively. The chapter focuses on eigenfunctions, and in particular, on stationary states. It presents several illustrations of the fact that there frequently are more than one linearly independent energy eigenfunction belonging to an energy eigenvalue.
