Scattering Theory in Quaternionic Quantum Mechanics and T-violation

Stephen L. Adler

Abstract In this chapter we develop methods, both exact and approximate, for timedependent problems (Adler, 1988), which complement the methods for stationary state problems given in Chapter 5 and their application to scattering theory in Chapter 6. We begin by giving the general equations for time-dependent perturbation theory in quaternionic quantum mechanics. By making an appropriate choice of initial conditions, these equations are applied successively to the problems of scattering theory and of decaying state theory. We next discuss the use of the interaction and Heisenberg pictures, particularly in the context of the quaternionic forced harmonic oscillator. We conclude by briefly discussing the use of quaternionic quantum mechanics as a model for time reversal violation in elementary particle physics (Adler, l 986a,b).

G. Scolarici, Luigi Solombrino

František Jenč

Stephen L. Adler

Abstract We proceed in this chapter to discuss scattering theory and related aspects of the bound-state problem in quaternionic quantum mechanics. We begin with a detailed discussion of a simple one-dimensional example, the delta function potential model. From this model will emerge the result (Adler, 1988) that will be the principal theme of this and the succeeding two chapters: with the standard ray representative choice of Sec. 4.2, for short-range potentials the asymptotic scattering states and the S-matrix in quaternionic quantum mechanics are always complex ℂ(1, i).

Stephen L. Adler