Hamilton-Jacobi equation

[′ham·əl·tən jə′kō·bē i‚kwā·zhən]

(mathematics)

A particular partial differential equation useful in studying certain systems of ordinary equations arising in the calculus of variations, dynamics, and optics: H (q₁, …, q_n, ∂φ/∂ q₁, …, ∂φ/∂ q_n, t) + ∂φ/∂ t = 0, where q₁, …, q_nare generalized coordinates, t is the time coordinate, H is the Hamiltonian function, and φ is a function that generates a transformation by means of which the generalized coordinates and momenta may be expressed in terms of new generalized coordinates and momenta which are constants of motion.

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References in periodicals archive

This general relativistic Hamilton-Jacobi equation becomes a scalar wave equation via the transformation to eliminate the squared first derivative, i.e., by defining the wave function [PSI] (q, p, t) of position q, momentum p, and time t as

Update on Pluto and its 5 moons obeying the quantization of angular momentum per unit mass constraint of quantum celestial mechanics

Identifying [bar.p] with [nabla]S and comparing with the Hamilton-Jacobi equation:

On Inhomogeneous Metamaterials Media: A New Alternative Method for Analysis of Electromagnetic Fields Propagation

(b) Higher-order WKB corrections: Using WKB approximation method, the lowest order of the equation of motion describing a particle moving in the black hole gives the Hamilton-Jacobi equation. The WKB approximation breaks down when the de Broglie wavelength of the particle, [[lambda].sub.p] ~ h/E, becomes comparable to the horizon of black hole, [r.sub.H].

Covariant GUP Deformed Hamilton-Jacobi Method

By taking into account the effect of GUP, in a curved spacetime, the revised Hamilton-Jacobi equation for the motion of scalar particles can be expressed as [26]

Remark on Remnant and Residue Entropy with GUP

The main aim of this paper is to investigate thermal radiation from Klein-Gordon equation, Maxwell's electromagnetic field equations, Dirac particles, and also nonthermal radiation of Hamilton-Jacobi equation in general nonstationary black hole.

Quantum Radiation Properties of General Nonstationary Black Hole

At the classical limit (h [right arrow] 0) Q vanishes and (4) reduces to the Hamilton-Jacobi equation. For this reason, Bohm [1] suggested that S is the classical action function, which relates to the actual velocity, v = [nabla]S /m, of the particle.

Phenomenological derivation of the Schrodinger equation

In this paper, we adopt a simple and effective method (i.e., Hamilton-Jacobi equation) to analyze the Hawking radiation of the regular phantom BH.

Gravitational Quasinormal Modes of Regular Phantom Black Hole

The Hamilton-Jacobi equation is derived for such motion and the effects of the curvature upon the quantization are analyzed, starting from a generalization of the Klein-Gordon equation in curved spaces.

Covariance, curved space, motion and quantization

Recall that the QCM general wave equation derived from the general relativistic Hamilton-Jacobi equation is approximated by a Schrodinger-like wave equation and that a QCM quantization state is completely determined by the system's total baryonic mass M and its total angular momentum [H.sub.[summation]].

Cosmological redshift interpreted as gravitational redshift

When the above expression for the Weyl scalar curvature (Bohm's quantum potential given in terms of the ensemble density) is inserted into the Hamilton-Jacobi equation, in conjunction with the continuity equation, for a momentum given by [p.sub.k] = [[partial derivative].sub.k]S, one has then a set of two nonlinear coupled partial differential equations.

On nonlinear quantum mechanics, Brownian motion, Weyl geometry and fisher information

which is therefore but another form taken by the KG equation (as expected from the fact that the KG equation is the quantum equivalent of the Hamilton-Jacobi equation).

Fractality field in the theory of scale relativity