DOI: 10.1063/1.533255. Structure and properties of Hughston’s stochastic extension of the Schrödinger equation

Structure and properties of Hughston’s stochastic extension of the Schrödinger equation

10.1063/1.533255

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

Abstract

Hughston has recently proposed a stochastic extension of the Schrödinger equation, expressed as a stochastic differential equation on projective Hilbert space. We derive new projective Hilbert space identities, which we use to give a general proof that Hughston’s equation leads to state vector collapse to energy eigenstates, with collapse probabilities given by the quantum mechanical probabilities computed from the initial state. We discuss the relation of Hughston’s equation to earlier work on norm-preserving stochastic equations, and show that Hughston’s equation can be written as a manifestly unitary stochastic evolution equation for the pure state density matrix. We discuss the behavior of systems constructed as direct products of independent subsystems, and briefly address the question of whether an energy-based approach, such as Hughston’s, suffices to give an objective interpretation of the measurement process in quantum mechanics.

Bibliography

Adler, S. L., & Horwitz, L. P. (2000). Structure and properties of Hughstonâs stochastic extension of the SchrÃ¶dinger equation. Journal of Mathematical Physics, 41(5), 2485â2499.

Authors 2

Stephen L. Adler (first)
Lawrence P. Horwitz (additional)

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Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:07 a.m.)
Deposited	2 years, 1 month ago (July 21, 2023, 8:35 p.m.)
Indexed	4 weeks ago (Aug. 6, 2025, 9:37 a.m.)
Issued	25 years, 4 months ago (May 1, 2000)
Published	25 years, 4 months ago (May 1, 2000)
Published Print	25 years, 4 months ago (May 1, 2000)

Funders 0

None

BibTeX

@article{Adler_2000, title={Structure and properties of Hughston’s stochastic extension of the Schrödinger equation}, volume={41}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.533255}, DOI={10.1063/1.533255}, number={5}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Adler, Stephen L. and Horwitz, Lawrence P.}, year={2000}, month=may, pages={2485–2499} }

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