We can not ignore the the wide range of physical phenomena which classical physics describes well. The correspondence principle emphasizes these successes. The correspondence principle is the recognition that any valid theory must be able to describe the phenomena of classical physics which we experience every day. Using this simple principle, one can impose surprisingly strong constraints and conditions on our new, more fundamental, quantum theory. This procedure ensures that quantum theory is consistent with the empirical observations of classical physics.
The particular phenomena with which we shall impose consistency in this set of notes is the fact that, as J.J. Thomson's observed, the electrons in cathode-ray tube experiments follow trajectories governed by Newton's law, F=ma. The fact that electrons follow Newtonian trajectories must be reconciled with the fact that they exhibit wave behavior with a wavelength given by (1) above.