In 1931 Schrödinger tried unsuccessfully to probabilistically derive his wave equation. We show that, after some improvements, his program yields two versions of stochastic mechanics. The first one coincides with Nelson stochastic mechanics, the second with the imaginary-time version of this theory, whose existence was unknown. The construction is founded on a variational approach inspired by Yasue.

• Received 24 June 1985

DOI:https://doi.org/10.1103/PhysRevA.33.1532