section_path: Mathematical formulation/Equivalence between formulations
section_name: Equivalence between formulations
paragraph_text: Equivalence between formulations
  
  There are many mathematically equivalent formulations of quantum mechanics. One of the oldest and most common is the " transformation theory " proposed by Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics – matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). An alternative formulation of quantum mechanics is Feynman 's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over all possible classical and non-classical paths between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics.