Elaborating on M. Pavon, J. Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechan- ics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kine- matics, the problem of the Schr ̈odinger bridge. This gives a profound meaning to what was observed by Schr ̈odinger in 1931 concerning Schr ̈odinger bridges: “Merkwu ̈rdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen”.
Quantum Schroedinger bridges
PAVON, MICHELE
2002
Abstract
Elaborating on M. Pavon, J. Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechan- ics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kine- matics, the problem of the Schr ̈odinger bridge. This gives a profound meaning to what was observed by Schr ̈odinger in 1931 concerning Schr ̈odinger bridges: “Merkwu ̈rdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen”.
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