Saxon-Hutner theorem via matrix exponential

Abstract

Making use of the well-known one-to-one correspondence between real localized potentials and transfer matrices, the Saxon-Hutner conjecture is reformulated initially as a group-theoretical and consequently as a Lie-algebraic problem. A very basic Lie theory, in conjunction with time-reversal symmetry of the time-independent Schrödinger equation, leads to several novel fairly general conditions which ensure the validity of the Saxon-Hutner theorem.