In this module, we will study the phenomena that led to the development of quantum mechanics, in roughly chronological order. This is to help you understand where the formalism of quantum mechanics comes from. Despite their importance in the development of quantum mechanics, many of the phenomena described here will not be rederived from quantum mechanics later in the course because their full treatment is quite advanced, e.g., requiring a fully quantum treatment of the electromagnetic field. You will meet them again in more advanced quantum mechanics courses. The exception is the derivation of the spectrum of the hydrogen atom, which is one of the crowning achievements of theoretical physics, and which we will obtain from quantum mechanics by the end of the course.
Old Quantum Theory
The theory developed in the period from 1900 to 1925 is called the old quantum theory. It was not a coherent or well-defined theory, but rather consisted of a set of ad-hoc modifications to classical physics that could lead to contradictions if not applied judiciously. These ad-hoc modifications were needed to account for several observed phenomena that defied explanation in terms of classical physics. By the end of this period, it was clear that a new physical theory was needed. The timeline of the old quantum theory is as follows:
1900: Max Planck solves the puzzle of blackbody radiation by positing that matter and radiation can only exchange energy in chunks, later called “quanta”.
1905: Einstein solves the puzzle of the photoelectric effect by positing that radiation only exists in discrete chunks, or particles, later called “photons”.
1913: Neils Bohr derives the spectrum of the hydrogen atom by positing that the electron orbiting the proton has a discrete angular momentum.
1923: The Compton effect confirms that electromagnetic waves have “particle-like” properties.
1923: de Broglie proposes “matter waves” — matter particles like electrons sometimes behave like waves.
The Development of Quantum Mechanics
Everyone knew that the old quantum theory was not a consistent theory of physics, but its predictions were rapidly confirmed. The race was on to develop a new theory of physics, and the first breakthrough came in 1925.
1925: Werner Heisenberg proposes matrix mechanics. This is a completely new theory meant to replace classical mechanics.
1926: Erwin Schrödinger proposes wave mechanics. Initially, this was thought to be a rival, different theory to matrix mechanics. It quickly gained popularity because its mathematics was more familiar to physicists than that of matrix mechanics.
1927 was a busy year:
Heisenberg proposes the uncertainty principle.
Max Born introduces probability into wave mechanics.
de Broglie's matter wave hypothesis is confirmed in experiments.
1927-
1935: A series of books and papers by people including Schrödinger, Paul Dirac, and John von Neumann, show that matrix mechanics and wave mechanics are equivalent, i.e., they always make the same predictions and are just different ways of writing down the same theory.