  We present a new formalism for describing solutions of the one-dimensional
stationary Schr\"odinger equation in terms of the Lie group SL(3,C) and its Lie
algebra. In this formalism, we obtain a universal expression for the Green
function which can be used in any representation of SL(3,C) and also
expressions for various quantities involving products of Green functions.
Specifically, we introduce an infinite-dimensional representation of SL(3,C)
that provides a natural description of multiple scattering of waves. Using this
particular representation, we can derive formulas which are useful for the
analysis of the Green function.
