Momentum in stochastic quantum mechanics

D. de Falco, S. De Martino, Silvio De Siena

Thomas Schuermann

Simon Golin

Position–momentum uncertainty in Nelson’s stochastic mechanics [Phys. Rev. 150, 1079 (1966)] has previously been investigated by de la Peña-Auerbach and Cetto [Phys. Lett. A 39, 65 (1972)]. In this paper their result is generalized, and full equivalence between the uncertainty relations in stochastic mechanics and conventional quantum mechanics is established. Force–momentum uncertainty is also considered.

Tetsuya Misawa

Quite recently, a symmetric stochastic calculus of variations was proposed to formulate canonical stochastic dynamics, which is an extension of Nelson’s stochastic mechanics. In this article a ‘‘Noether’s theorem’’ is formulated within this calculus of variations. Conservation laws of momentum, angular momentum, and energy are proved, which are related with the same laws in quantum mechanics.

L. de la Peña-Auerbach