The squared eigenstates of the sine–Gordon eigenvalue problem

Abstract

An analysis of the squared sine–Gordon eigenvalue problem in laboratory coordinates is presented. It is shown that unlike the unsquared laboratory coordinate eigenvalue problem, the squared laboratory coordinate eigenvalue problem may be cast into the form of a standard eigenvalue problem, wherein an eigenvalue independent operator operating on an eigenfunction generates the eigenvalue. With this form, it becomes rather elementary to obtain the squared-eigenfunction expansion of the sine–Gordon potentials as well as to demonstrate closure.