ODD-EVEN FACTORIZATION RESULTS FOR EIGENVALUE PROBLEMS

It is demonstrated that, in each of two problems which involve physica l symmetry, the appropriate eigenvalue equation factorizes into two eq uations, one of which corresponds to solutions which are even function s of the independent variable, and the other to solutions which are od d functions. The first situation involves a two-point boundary value p roblem and a linear differential equation. The second involves the eig envalue problem for a matrix which is symmetric about both of its diag nols.