From canonical transformations to transformation theory, 1926-1927: The road to Jordan's Neue Begründung

We sketch the development from matrix mechanics as formulated in the Dreimännerarbeit of Born, Heisenberg, and Jordan, completed in late 1925, to transformation theory developed independently by Jordan and Dirac in late 1926. Focusing on Jordan, we distinguish three strands in this development: the implementation of canonical transformations in matrix mechanics (the main focus of our paper), the clarification of the relation between the different forms of the new quantum theory (matrix mechanics, wave mechanics, q-numbers, and operator calculus), and the generalization of Born's probability interpretation of the Schrödinger wave function. These three strands come together in a two-part paper by Jordan published in 1927, "On a new foundation [neue Begründung] of quantum mechanics.".