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The Quantum Hamilton–Jacobi Equation and the Link Between Classical and Quantum Mechanics
Quanta, 2022 We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton–Jacobi equation. While in the classically forbidden regions these quantum quantities directly tend to the classical ones, this is not the case in the allowed regions.
Fusco Girard, Mario, Girard, Mario Fusco
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ANALYTICAL MECHANICS IN STOCHASTIC DYNAMICS: MOST PROBABLE PATH, LARGE-DEVIATION RATE FUNCTION AND HAMILTON–JACOBI EQUATION [PDF]
International Journal of Modern Physics B, 2012 Analytical (rational) mechanics is the mathematical structure of Newtonian deterministic dynamics developed by D'Alembert, Lagrange, Hamilton, Jacobi, and many other luminaries of applied mathematics. Diffusion as a stochastic process of an overdamped individual particle immersed in a fluid, initiated by Einstein, Smoluchowski, Langevin and Wiener ...
Ge, Hao, Qian, Hong
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Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2021 In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces.
Vasyl Kovalchuk +2 more
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Diffusion Effect in Quantum Hydrodynamics
Axioms, 2022 In this paper, we introduce (at least formally) a diffusion effect that is based on an axiom postulated by Werner Heisenberg in the early days of quantum mechanics.
Moise Bonilla-Licea +2 more
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Hamilton-Jacobi and Lagrange Formulations of Relativistic Quantum Mechanics Wave Equations with Solutions with Only-Positive and Only-Negative Kinetic Energies [PDF]
Journal of Modern Physics, 2022 Abstract Using the Hamilton-Jacobi and the Lagrange formalisms, a pair of relativistic quantum mechanics equations are obtained. These equations, in contrast with the Klein-Gordon and other relativistic quantum mechanics equations, have no solutions with both positive and negative kinetic energies. The equation with solutions with only positive
Luis Grave de Peralta +1 more
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A unified framework for mechanics: Hamilton–Jacobi equation and applications [PDF]
Nonlinearity, 2010 In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical systems...). We recover all these, in principle, different cases using a unified framework based on skew-symmetric ...
Balseiro, P. +3 more
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Phase Shifts and the Quantum-Mechanical Hamilton—Jacobi Equation [PDF]
The Journal of Chemical Physics, 1965 A method of obtaining absolute phase shifts by integration of the quantum-mechanical Hamilton—Jacobi equation is developed and applied to the example of particles interacting through a Lennard-Jones potential. A new expression for the absolute phase shift is obtained in terms of an irregular solution of the Schrödinger equation.
Donald J. Kouri, C. F. Curtiss
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Entropy, 2020 We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom: “trainable” variables (e.g., bias vector or weight matrix) and “hidden” variables (e.g.,
Vitaly Vanchurin
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Bohm's potential, classical/quantum duality and repulsive gravity
Physics Letters B, 2019 We propose the notion of a classical/quantum duality in the gravitational case (it can be extended to other interactions). By this one means exchanging Bohm's quantum potential for the classical potential VQ↔V in the stationary quantum Hamilton–Jacobi ...
Carlos Castro Perelman
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Representation Formula for Solutions of Eikonal Type Equations
Nonlinear Analysis, 2001 Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for ...
Gintautas Gudynas
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