| dc.description.abstract | Quantum mechanics is one of the crowning achievements of human thought. There
is no theory that is more successful in predicting phenomena over such a wide range
of situations—and with such accuracy—than quantum mechanics. From the basic
principles of chemistry to the working of the semiconductors in your mobile phone,
and from the Big Bang to atomic clocks, quantum mechanics comes up with the
goods. At the same time, we still have trouble pinpointing exactly what the theory
tells us about nature. Quantum mechanics is hard, but perhaps not as hard as you
think. Let us compare it to another great theory of physics: electromagnetism.
When we teach electricity and magnetism in school and university, we start with
simple problems involving point charges and line currents. We introduce Coulomb’s
law, the law of Biot and Savart, the Lorentz force, and so on. After working through
some of the most important consequences of these laws, we finally arrive at
Maxwell’s equations. Advanced courses in electrodynamics then take over and
explore the consequences of this unification, treating such topics as waveguides,
gauge invariance, relativity. The pedagogical route is going from the simple, tangible
problems to the general and abstract theory. You need to know quite a bit of
electromagnetism and vector calculus before you can appreciate the beauty of
Maxwell’s equations.
The situation in teaching quantum mechanics is generally quite different. Instead
of simple experimentally motivated problems, a first course in quantum mechanics
often takes a historical approach, describing Planck’s solution of black-body
radiation, Einstein’s explanation of the photoelectric effect, and Bohr’s model for
the atom from 1913. This is then followed by the introduction of the Schrödinger
equation. The problem is that appreciating Schrödinger’s equation requires a degree
of familiarity with the corresponding classical solutions that most students do not
yet have at this stage. As a result, many drown in the mathematics of solving the
Schrödinger equation and never come to appreciate the subtle and counterintuitive
aspects of quantum mechanics as a fundamental theory of nature. | en_US |
