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).
Binding energies of the ground
1S states of the alkali negative ions are calculated using the coupled equations of scattering theory, based on semiempirical effective potentials for the neutral atoms. An additional true bound state with configuration
3P lying just below the first excited state of the neutral atom is predicted for every species except ${\mathrm{Li}}^{\ensuremath{-}}$.