This paper by Barry Simon analyzes a class of pairs of positive self-adjoint operators \(A\) and \(B\) where the limit of \(A + \lambda B\) as \(\lambda \downarrow 0\) is an operator \(A_p \neq A\). Simon discusses Klauder's phenomenon, which involves the eigenvalues and eigenvectors of \(A + \lambda B\) not converging to those of \(A\) and \(A_p\) but rather to different functions. The analysis is grounded in the techniques of quadratic forms and strong resolvent convergence. Simon provides a detailed explanation of this phenomenon, showing that it occurs when the intersection of the form domains of \(A\) and \(B\) is not a form core for \(A\). The paper includes several examples to illustrate the theory, such as operators with singular perturbations and different boundary conditions, and concludes with a discussion on the limitations of the form sum approach.This paper by Barry Simon analyzes a class of pairs of positive self-adjoint operators \(A\) and \(B\) where the limit of \(A + \lambda B\) as \(\lambda \downarrow 0\) is an operator \(A_p \neq A\). Simon discusses Klauder's phenomenon, which involves the eigenvalues and eigenvectors of \(A + \lambda B\) not converging to those of \(A\) and \(A_p\) but rather to different functions. The analysis is grounded in the techniques of quadratic forms and strong resolvent convergence. Simon provides a detailed explanation of this phenomenon, showing that it occurs when the intersection of the form domains of \(A\) and \(B\) is not a form core for \(A\). The paper includes several examples to illustrate the theory, such as operators with singular perturbations and different boundary conditions, and concludes with a discussion on the limitations of the form sum approach.