Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Derivation of the Wave Function Collapse in the Context of Nelson's Stochastic Mechanics

Pavon, M

Published Jan 1, 1999• 12 citations
OpenAlex

Abstract

The von Neumann collapse of the quantum mechanical wavefunction after a position measurement is derived by a purely probabilistic mechanism in the context of Nelson's stochastic mechanics.

Related papers

Derivation of the wave function collapse in the context of Nelson’s stochastic mechanics

Michele Pavon

The von Neumann collapse of the quantum mechanical wave function after a position measurement is derived by a purely probabilistic mechanism in the context of Nelson’s stochastic mechanics.

arXiv:quant-ph/9912015•Journal of Mathematical Physics•Nov 1, 1999•14 citations

A note on the quantum measurement problem

N. David Mermin

The idea that wave-function collapse is a physical process stems from a misunderstanding of probability and the role it plays in quantum mechanics.

arXiv:2206.10741•Jun 21, 2022•0 citations

Quantum Schroedinger bridges

Michele Pavon

Elaborating on M. Pavon, J.Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechanics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kinematics, the problem of the Schroedinger bridge. This gives a profound meaning to what was observed by Schroedinger in 1931 concerning Schroedinger bridges: "Merkwuerdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen".

arXiv:quant-ph/0306052•Jun 6, 2003•0 citations

Distinguishing Projective (von Neumann) Measurement from Unitary Transformations in Quantum Mechanics and Computing

Chinnaraji Annamalai

In quantum mechanics and quantum information science, state evolution occurs via two fundamental mechanisms: deterministic unitary gate transformations and projective (von Neumann) measurements. This paper formalizes the three mathematical and physical pillars that differentiate projective measurements from unitary operations: stochastic behavior governed by the Born rule, non-linearity introduced via wave function collapse normalization, and operational irreversibility. It provides rigorous mathematical derivations for state update rules, explores the role of eigenvalues and observables, and demonstrates the non-linearity of projective measurements through concrete mathematical examples.

•Sep 23, 2026•0 citations

The collapses of wave functions

Boris B. Kadomtsev, Михаил Борисович Кадомцев

The collapse of the wave function has recently reemerged as a subject of extensive discussion in the quantum mechanical literature. In the present paper, wave function collapses occuring during the irreversible evolution of complex quantum systems, including those involved in measurement procedures, are described.

Physics-Uspekhi•Jun 30, 1996•21 citations

Stochastic Methods and Dynamical Wave-function Collapse

Angelo Bassi, Kinjalk Lochan, Seema Satin +2 more

This brief article reviews stochastic processes as relevant to dynamical models of wave-function collapse, and is supplemental material for the review article arXiv:1204.4325

arXiv:1212.5535•Dec 21, 2012•1 citation
Elaborating on M. Pavon, J.Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechanics that produces the von Neumann wave packet reduction after a position measurement. This stochastic control problem parallels, with a different kinematics, the problem of the Schroedinger bridge. This gives a profound meaning to what was observed by Schroedinger in 1931 concerning Schroedinger bridges: "Merkwuerdige Analogien zur Quantenmechanik, die mir sehr des Hindenkens wert erscheinen".
In quantum mechanics and quantum information science, state evolution occurs via two fundamental mechanisms: deterministic unitary gate transformations and projective (von Neumann) measurements. This paper formalizes the three mathematical and physical pillars that differentiate projective measurements from unitary operations: stochastic behavior governed by the Born rule, non-linearity introduced via wave function collapse normalization, and operational irreversibility. It provides rigorous mathematical derivations for state update rules, explores the role of eigenvalues and observables, and demonstrates the non-linearity of projective measurements through concrete mathematical examples.