  The hydrogen atom perturbed by a constant 1-dimensional weak quadratic
potential $\lambda z^2$ is solved at first-order perturbation theory using the
eigenstates of the total angular momentum operator - the coupled basis.
Physical applications of this result could be found, for example, in the study
of a quadratic Zeeman effect weaker than fine-structure effects, or in a
perturbation caused by instantaneous generalised van der Waals interactions.
