Amplitude phase-space model for quantum mechanics
type: Item
instance of: scholarly article
title: Amplitude phase-space model for quantum mechanics
zbMATH Open document ID: 0563.60099
DOI: 10.1007/BF00670802
author: Stan Gudder
published in: International Journal of Theoretical Physics
publication date: 1985-01-01T00:00:00Z
review text: We show that there is a close relationship between quantum mechanics and ordinary probability theory. The main difference is that in quantum mechanics the probability is computed in terms of an amplitude function, while in probability theory a probability distribution is used. Applying this idea, we then construct an amplitude model for quantum mechanics on phase space. In this model, states are represented by amplitude functions and observables are represented by functions on phase space. If we now postulate a conjugation condition, the model provides the same predictions as conventional quantum mechanics. In particular, we obtain the usual quantum marginal probabilities, conditional probabilities and expectations. The commutation relations and uncertainty principle also follow. Moreover Schrödinger's equation is shown to be an averaged version of Hamilton's equation in classical mechanics.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 60H99
zbMATH DE Number: 3897995
zbMATH Keywords: relationship between quantum mechanics and ordinary probability theory
zbMATH Keywords: quantum marginal probabilities
zbMATH Keywords: Schrödinger's equation
zbMATH Keywords: Hamilton's equation
MaRDI profile type: Publication
cites work: Space-Time Approach to Non-Relativistic Quantum Mechanics
cites work: Q5569065
cites work: Finite quantum processes
cites work: Markoff chains, Wiener integrals, and quantum theory
cites work: On the Quantum Correction For Thermodynamic Equilibrium
full work available at URL: https://doi.org/10.1007/bf00670802
OpenAlex ID: W2067843410
description: scientific article; zbMATH DE number 3897995