DISCRETE SYMMETRIES IN QUANTUM SCATTERING

Using the discrete symmetries of the Klein-Gordon, Dirac, and Schrodin ger wave equations, we obtain from one solution, considered as a funct ion of the quantum numbers and the parameters of the potentials, three other solutions. Taken together, these solutions form two complete se ts of solutions of the wave equation. The coefficients of the linear r elations between the functions of these sets - the connection coeffici ents - are related in a simple manner to the wave transmission and ref lection amplitudes. By virtue of the discrete symmetries of the wave e quation, the connection coefficients satisfy certain symmetry relation s. We show that in a number of simple cases, the behavior of the wave function near the center of formation of an additional wave determines the amplitude of the wave that is formed at infinity.