[AntonioLao]

Dirac wrote a paper in Physikalische Zeitschrift der Sowjetunion, Band 3, Heft 1 (1933). The title in English is ‘The Lagrangian in Quantum Mechanics’ and the following are complete excerpts of the 1st two paragraphs.

Quantum mechanics was built up on a foundation of analogy with the Hamiltonian theory of classical mechanics. This is because the classical notion of canonical coordinates and momenta was found to be one with a very simple quantum analogue, as a result of which the whole of the classical Hamiltonian theory, which is just a structure built up on this notion, could be taken over in all its details into quantum mechanics.

Now there is an alternative formulation for classical dynamics, provided by the Lagrangian. This requires one to work in terms of coordinates and velocities instead of coordinates and momenta. The two formulations are, of course, closely related, but there are reasons for believing that the Lagrangian one is more fundamental.