Resonance widths and positions by an algebraic approach

The use of nonunitary discrete, irreducible representations of Lie algebras is proposed as a method for the determination of widths and energies of resonances. The method is illustrated by explicit application to three kinds of resonances: in transmission over a well, in transmission over a barrier, and in barrier penetration for a family of one-dimensional potentials. The same procedure is also useful in an algebraic approach to scattering by a complex (optical) potential, and for parametrization of the resonant contribution to the scattering matrix.