Wave Theory of Lattice-Directed Trajectories. I. The Basic Theory

The wave equation of a relativistic lattice-directed projectile is solved by separation of variables and assuming a continuum approximation to the interaction potential. We obtain plane-wave solutions along the low-index direction and a band spectrum of "transverse-energy" values corresponding to two-dimensional Bloch states in the plane normal to the simple direction. It is shown that the actual periodicity of the assumed continuum wall causes a dechanneling mechanism. The theory contains diffraction theory and the classical theory of lattice-directed trajectories in its limits.