The nonlocal advection diffusion equation and the two-slit experiment in
quantum mechanics
- URL: http://arxiv.org/abs/2303.10061v1
- Date: Fri, 17 Mar 2023 15:44:10 GMT
- Title: The nonlocal advection diffusion equation and the two-slit experiment in
quantum mechanics
- Authors: Glenn Webb
- Abstract summary: The state variable of the equation is the probability density function of particle positions.
The model is compared to the Schr"odinger equation model of the experiment.
- Score: 0.0
- License: http://creativecommons.org/publicdomain/zero/1.0/
- Abstract: A partial differential equation model is analyzed for the two-slit experiment
of quantum mechanics. The state variable of the equation is the probability
density function of particle positions. The equation has a diffusion term
corresponding to the random movement of particles, and a nonlocal advection
term corresponding to the movement of particles in the transverse direction
perpendicular to their forward movement. The model is compared to the
Schr\"odinger equation model of the experiment. The model supports the ensemble
interpretation of quantum mechanics.
Related papers
- Quantum Particle Statistics in Classical Shallow Water Waves [4.995343972237369]
We show that when locally oscillating particles are guided by real wave gradients, particles may exhibit trajectories of alternating periodic or chaotic dynamics.
The particle probability distribution function of this analogy reveals the quantum statistics of the standard solutions of the Schr"odinger equation.
arXiv Detail & Related papers (2024-09-29T09:40:19Z) - Quantum mechanics without quantum potentials [0.0]
Non-locality in quantum mechanics can be resolved by considering relativistically covariant diffusion in spacetime.
We introduce the concept of momentum equilinear to replace the second-order Bohm-Newton equations of motion.
arXiv Detail & Related papers (2024-01-08T18:51:38Z) - Open Quantum Systems with Kadanoff-Baym Equations [0.0]
We study quantum mechanical fermionic particles exhibiting one bound state within a one-dimensional attractive square-well potential in a heat bath of bosonic particles.
For this open quantum system we formulate the non-equilibrium Kadanoff-Baym equations for the system particles.
The corresponding spatially imhomogeneous integro-differential equations for the one-particle Greens's function are solved numerically.
arXiv Detail & Related papers (2023-08-15T09:19:21Z) - A generalized scattering theory in quantum mechanics [1.14219428942199]
In quantum mechanics textbooks, a single-particle scattering theory is introduced.
A generalized Lippmann-Schwinger scattering equation is derived.
The transition probability of the scattering of two free particles is identical to that of the reciprocal process.
arXiv Detail & Related papers (2023-07-03T11:07:46Z) - Double-scale theory [77.34726150561087]
We present a new interpretation of quantum mechanics, called the double-scale theory.
It is based on the simultaneous existence of two wave functions in the laboratory reference frame.
The external wave function corresponds to a field that pilots the center-of-mass of the quantum system.
The internal wave function corresponds to the interpretation proposed by Edwin Schr"odinger.
arXiv Detail & Related papers (2023-05-29T14:28:31Z) - Exact quantum-mechanical equations for particle beams [91.3755431537592]
These equations present the exact generalizations of the well-known paraxial equations in optics.
Some basic properties of exact wave eigenfunctions of particle beams have been determined.
arXiv Detail & Related papers (2022-06-29T20:39:36Z) - Dispersive readout of molecular spin qudits [68.8204255655161]
We study the physics of a magnetic molecule described by a "giant" spin with multiple $d > 2$ spin states.
We derive an expression for the output modes in the dispersive regime of operation.
We find that the measurement of the cavity transmission allows to uniquely determine the spin state of the qudits.
arXiv Detail & Related papers (2021-09-29T18:00:09Z) - Schrodinger's Equation is Universal, Dark Matter and Double Diffusion [0.0]
This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum.
The main result of the paper shows that the colliding two particle classical Hamiltonian energy can be represented in four weighted individual particle.
The Schrodinger equation can also be used to represent corrections for Newton's equation and suggests a user profile to be used in the search for Dark Matter.
arXiv Detail & Related papers (2021-05-05T11:02:37Z) - Evolution of a Non-Hermitian Quantum Single-Molecule Junction at
Constant Temperature [62.997667081978825]
We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments.
We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
arXiv Detail & Related papers (2021-01-21T14:33:34Z) - Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered.
Operators of the form $hatcal H=hatA+ihatB$ are described.
Rigorous analytical analysis is performed for both wave and Green's functions.
arXiv Detail & Related papers (2020-10-13T15:50:49Z) - External and internal wave functions: de Broglie's double-solution
theory? [77.34726150561087]
We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory.
The principle is to decompose the evolution of a quantum system into two wave functions.
For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
arXiv Detail & Related papers (2020-01-13T13:41:24Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.