The spherical Whittaker Inversion Theorem and the quantum non-periodic Toda Lattice

Abstract: In this paper the spherical case of the Whittaker Inversion Theorem is given a relatively self-contained proof. This special case can be used as a help in deciphering the handling of the continuous spectrum in the proof of the full theorem. It also leads directly to the solution of the quantum non-periodic Toda Lattice. This is also explained in detail in this paper.