Spectral decomposition of the operator p2-q2

Abstract

It is shown that the operator p2–q2 has a continuous spectrum extending from −∞ to +∞. The expansion of an arbitrary function with respect to the eigenfunctions is given. The action of the operators q and p on the eigenfunctions can be written explicitly by means of symbolic formulae. Finally, an alternative method for studying the behaviour of self-accelerating wave packets is given.