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

Physics Letters A

Short-time quantum propagator and Bohmian trajectories

Maurice A. de Gosson, Basil J. Hiley

Published Sep 10, 2013• 17 citations
Publisher

Abstract

We begin by giving correct expressions for the short-time action following the work Makri-Miller. We use these estimates to derive an accurate expression modulo [Formula: see text] for the quantum propagator and we show that the quantum potential is negligible modulo [Formula: see text] for a point source, thus justifying an unfortunately largely ignored observation of Holland made twenty years ago. We finally prove that this implies that the quantum motion is classical for very short times.

DOI
10.1016/j.physleta.2013.08.031

Related papers

Short Time Quantum Propagator and Bohmian Trajectories

Maurice A. de Gosson, Basil J. Hiley

We begin by giving correct expressions for the short-time action; following the work of one of us and Makri--Miller. We use these estimates to derive a correct expression modulo modulo delta(t)sqr for the quantum propagator and we show that the quantum potential is negligible modulo delta(t)sqr for a point source. We finally prove that this implies that the quantum motion is classical for very short times.

arXiv:1304.4771•Apr 17, 2013•9 citations

The symplectic egg in classical and quantum mechanics

Maurice A. de Gosson

We begin by giving correct expressions for the short-time action; following the work of one of us and Makri-Miller.We use these estimates to derive a correct expression modulo ∆t 2 for the quantum propagator and we show that the quantum potential is negligible modulo ∆t 2 for a point source.We finally prove that this implies that the quantum motion is classical for very short times.

American Journal of Physics•Apr 16, 2013•23 citations

A note on the short-time quantum propagator

Sanayei, Ali

In the Feynman formalism of quantum mechanics one encounters a postulate, namely, that the propagator in an infinitesimal time-interval is the classical wave function. This postulate, which was later studied thoroughly by Holland, was recently highlighted by using the improved Makri-Miller propagator. The present note, whose conclusion is in agreement with that recent achievement, demonstrates that the Heisenberg picture of quantum mechanics invariably includes the Feynman postulate and is able to yield a proof for it. In other words, by starting out from the Heisenberg picture, it is proved that when terms of second-order in time can be neglected, the dynamics of a system is classical.

arXiv:1404.0506•Apr 2, 2014•1 citation

Hamiltonian flows, short-time propagators and the quantum Zeno effect

Maurice A. de Gosson, Basil J. Hiley

In a recent paper we have examined the short-time propagator for the Schrödinger equation of a point source. An accurate expression modulo Δ t 2 for the propagator showed that it was independent of the quantum potential implying that the quantum motion is classical for very short times. In this paper we apply these results to the experiment of Itano, Heinzen, Bollinger and Wineland which demonstrates the quantum Zeno effect in beryllium. We show that the transition is inhibited because the applied continuous wave radiation suppresses the quantum potential necessary for the transition to occur. This shows there is no need to appeal to wave function collapse.

Journal of Physics Conference Series•Apr 14, 2014•1 citation

Short-Time Propagators and the Born–Jordan Quantization Rule

Maurice A. de Gosson

We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born-Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

arXiv:1506.00111•Entropy•Nov 10, 2018•7 citations

Bohmian Mechanics: Towards Illuminating The Quantum Potential

Matthew J. Brown

This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.

•Feb 20, 2018•1 citation
We begin by giving correct expressions for the short-time action following the work Makri-Miller. We use these estimates to derive an accurate expression modulo [Formula: see text] for the quantum propagator and we show that the quantum potential is negligible modulo [Formula: see text] for a point source, thus justifying an unfortunately largely ignored observation of Holland made twenty years ago. We finally prove that this implies that the quantum motion is classical for very short times.
In the Feynman formalism of quantum mechanics one encounters a postulate, namely, that the propagator in an infinitesimal time-interval is the classical wave function. This postulate, which was later studied thoroughly by Holland, was recently highlighted by using the improved Makri-Miller propagator. The present note, whose conclusion is in agreement with that recent achievement, demonstrates that the Heisenberg picture of quantum mechanics invariably includes the Feynman postulate and is able to yield a proof for it. In other words, by starting out from the Heisenberg picture, it is proved that when terms of second-order in time can be neglected, the dynamics of a system is classical.
In a recent paper we have examined the short-time propagator for the Schrödinger equation of a point source. An accurate expression modulo Δ t 2 for the propagator showed that it was independent of the quantum potential implying that the quantum motion is classical for very short times. In this paper we apply these results to the experiment of Itano, Heinzen, Bollinger and Wineland which demonstrates the quantum Zeno effect in beryllium. We show that the transition is inhibited because the applied continuous wave radiation suppresses the quantum potential necessary for the transition to occur. This shows there is no need to appeal to wave function collapse.
We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born-Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.
This thesis deals with the theoretical and experimental details of trying to understand \nand infer the quantum potential from Bohmian mechanics using Bohmian trajectories. In \nthis work, some of the key components of the history of Bohmian mechanics is given, a \ntheoretical explanation of how to measure the Bohmian potential, followed by an overview \nof the experimental apparatus and its components. Some tests of the experimental apparatus \nare then presented followed by a discussion of the results. Lastly, some interesting \nfollow up experiments are de ned and discussed. \n \nBohmian mechanics, while completely agreeing with quantum mechanics could not be \nmore di erent from the standard notions such as the fact that particles retain their classical \nidentity of a point like object that have de nite and causal trajectories. In this realm, rst \ndeveloped by de Broglie, these particles move and are guided by a wave, which turns out \nto be the wave function itself. Typically, the velocity of the particles anywhere in space \nis given by spatial derivatives of the phase of this wave and the energy content of the \nparticles is given by the temporal derivative. The trajectories can bend even when there \nare no outside (classical) forces that are acting on the objects. This is due to the fact that \nthese observations of Bohmian mechanics must conform to the standard measurements in \nquantum mechanics. \n \nOne detail that has gone unmeasured (in the sense of inference) in a laboratory setting, \nis the quantum potential (the mysterious force that moves particle to make sure they \nreproduce the measurements of quantum mechanics). Using the technique of measuring \nthe trajectories of photons, the question was asked, can the quantum potential for single \nphotons in the double slit be inferred? A setup has been built in order to try and answer this \nquestion using a single photon detecting camera and a heralding spontaneous parametric \ndown conversion source. Unfortunately, the quantum potential still goes unmeasured due \nto noise in the camera pictures destroying the integrity of the signal and an interesting \nproblem of trying to stitch together the quantum potential at the varying z-planes.