  We propose a new derivation of Time-Independent Perturbation Theory (PT) that
has a fundamental advantage over the usual derivations presented in textbooks
on Quantum Mechanics (QM): it is simpler and much shorter. As such, it can
provide an easier and quicker way for students to learn PT, than afforded by
current methods. In spite of that, our approach does not require the potentials
to be energy independent or the inverse free Green function $G_0^{-1}(E)$ to be
a linear function of energy $E$, as is the case in QM, and can be applied
directly to various extensions of QM including Relativistic QM, the
Bethe-Salpeter equation, and all kinds of quasipotential approaches in Quantum
Field Theory.
