Paul ( P. A. M.) Dirac formulated the most elegant version of the mathematical principles of quantum mechanics after hearing a lecture by
Werner Heisenberg on his new ideas of "matrix mechanics." Shortly after matrix mechanics,
Erwin Schrödinger developed his "wave mechanics" and showed it was equivalent to the Heisenberg picture.
Dirac combined both of these using a method from classical mechanics called Poisson brackets.
In his 1930 textbook
The Principles of Quantum Mechanics,
Paul Dirac introduced the concepts of
superposition and
indeterminacy using examples with polarized photons.
The examples suggest a very simple and inexpensive experiment that we call the
Dirac 3-polarizers experiment to demonstrate
the notions of quantum
states, the
preparation of quantum systems in states with known properties, the
superposition of states, the
measurement of various properties, the
projection or
representation of a state vector in another basis set of vectors, and the infamous "collapse" or "reduction" of the wave function and the resulting indeterminacy.
