RECONCILING  CLASSICAL  AND QUANTUM  MECHANICS

We now have a confusing situation where a particle like an electron can behave as a wave when it has momentum. The converse is also true, in that photons which normally exhibit wave behavior can exhibit the properties of particles, as demonstrated by the photoelectric effect. Quantum mechanics, using complex wave functions, allows predictions of electron behavior, but how do we reconcile this with classical mechanics which works, so well in describing everyday macroscopic events? Let’s draw a few conclusions to keep things straight.

● Classical physics such as Newtonian mechanics provides a very clear view of how macroscopic particles and everyday objects behave.

● Depending on the circumstances, quantum physics may best describe the properties and behaviors of subatomic particles such as electrons.

Of course, defining those circumstances is the key, but the situation here is identical to that encountered in kinematics. Consider the correspondence principle. From kinematics we know that as a particle or object approaches the speed of light, Newtonian mechanics ceases to describe the situation correctly and special relativity must be used. In a similar manner, classical mechanics works well for large, macroscopic objects, but as we delve into the area of the atom, quantum physics best describes situations arising there. Bohr devised the correspondence principle to reconcile classical and quantum mechanics. He stated that at small quantum numbers such as n = 1, 2, 3, . . . , the domain of interest for atomic transitions that emit light, quantum mechanics describes the situation best, but as n becomes larger, up to say 10,000, the predictions of quantum and classical theory will agree. In other words, at large quantum numbers, quantum mechanics simply reduces to classical physics. Returning to the example of hydrogen, classical physics predicts that the frequency of an emitted photon will be equal to the frequency of the electron’s revolution in orbit around the nucleus. Quantum mechanics uses the notion of transitions between energy levels. When considering a quantum number of n =2, quantum mechanics predicts the frequency of emitted photons with great accuracy, whereas classical mechanics fails. When a large quantum number of 10,000 is considered, we find that the classical and quantum mechanical approaches agree within a fraction of a percent.