The work that built on Schrödinger's equation relied on analogies to Hamiltonian mechanics. In 1933 Paul Dirac published a paper seeking an alternative formulation based on Lagrangian mechanics. He was motivated by the power of the action principle and the relativistic invariance of the action itself. Dirac was able to show that the wavefunctions probability amplitude at x 1 , t 2 was related to the amplitude at x 2 , t 2 through an complex exponential function of the action.