Application of first-order perturbation theory to the confined time of arrival problem

Abstract

We formulate the first-order perturbation theory to the Confined Quantum Time of Arrival Problem, and apply it with quantum systems with perturbed harmonic interaction. We then compare the calculated eigenvalues to the values obtained numerically, particularly using Nystrom and Clenshaw-Curtis method. We show that the results of perturbation theory agree with the numerical results and that the Clenshaw-Curtis method is more accurate than the Nystrom method.