Coherent states, Schrödinger equation, and the Hamilton–Jacobi equation

1995 ◽  
Vol 73 (7-8) ◽  
pp. 478-483
Author(s):  
Rachad M. Shoucri
Keyword(s):  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Hidden Variables ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Phase Variable ◽  
Independent Variable ◽  
Hamilton Jacobi Equation

The self-adjoint form of the classical equation of motion of the harmonic oscillator is used to derive a Hamiltonian-like equation and the Schrödinger equation in quantum mechanics. A phase variable ϕ(t) instead of time t is used as an independent variable. It is shown that the Hamilton–Jacobi solution in this case is identical with the solution obtained from the Schrödinger equation without the need to introduce the idea of hidden variables or quantum potential.

scholarly journals SYMMETRY REDUCTION OF BROWNIAN MOTION AND QUANTUM CALOGERO–MOSER MODELS

2012 ◽  
Vol 13 (01) ◽  
pp. 1250007
Author(s):  
SIMON HOCHGERNER
Keyword(s):  
Brownian Motion ◽  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Symmetry Reduction ◽  
Reduction Scheme ◽  
Polar Actions ◽  
Stochastic Setting ◽  
Hamilton Jacobi Equation

Let Q be a Riemannian G-manifold. This paper is concerned with the symmetry reduction of Brownian motion in Q and ramifications thereof in a Hamiltonian context. Specializing to the case of polar actions, we discuss various versions of the stochastic Hamilton–Jacobi equation associated to the symmetry reduction of Brownian motion and observe some similarities to the Schrödinger equation of the quantum–free particle reduction as described by Feher and Pusztai [10]. As an application we use this reduction scheme to derive examples of quantum Calogero–Moser systems from a stochastic setting.

scholarly journals The Equivalence Postulate of Quantum Mechanics, Dark Energy, and the Intrinsic Curvature of Elementary Particles

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Alon E. Faraggi
Keyword(s):  
Quantum Mechanics ◽  
Dark Energy ◽  
Schrödinger Equation ◽  
Jacobi Equation ◽  
Schrodinger Equation ◽  
Axiomatic Approach ◽  
Quantum Potential ◽  
Curvature Term ◽  
Cocycle Condition ◽  
Hamilton Jacobi Equation

The equivalence postulate of quantum mechanics offers an axiomatic approach to quantum field theories and quantum gravity. The equivalence hypothesis can be viewed as adaptation of the classical Hamilton-Jacobi formalism to quantum mechanics. The construction reveals two key identities that underlie the formalism in Euclidean or Minkowski spaces. The first is a cocycle condition, which is invariant underD-dimensional Möbius transformations with Euclidean or Minkowski metrics. The second is a quadratic identity which is a representation of theD-dimensional quantum Hamilton-Jacobi equation. In this approach, the solutions of the associated Schrödinger equation are used to solve the nonlinear quantum Hamilton-Jacobi equation. A basic property of the construction is that the two solutions of the corresponding Schrödinger equation must be retained. The quantum potential, which arises in the formalism, can be interpreted as a curvature term. The author proposes that the quantum potential, which is always nontrivial and is an intrinsic energy term characterising a particle, can be interpreted as dark energy. Numerical estimates of its magnitude show that it is extremely suppressed. In the multiparticle case the quantum potential, as well as the mass, is cumulative.

scholarly journals On the Asymptotics of the Schrödinger Equation Solutions and the Euler Model of an Ideal Fluid

2021 ◽  
Author(s):  
Владислав Хаблов
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Ideal Fluid ◽  
Jacobi Equation ◽  
Schrodinger Equation ◽  
Continuity Equation ◽  
Rotation Group ◽  
Potential Flows ◽  
Euler Model ◽  
Hamilton Jacobi Equation

In this paper we analyze the asymptotics of the Schrödinger equation solutions with respect to a small parameter ~. It is well known, that short- waveasymptoticstosolutionsofthisequationleadstothepairofequations— the Hamilton–Jacobi equation for the phase and the continuity equation. These equations coincide with the ones for the potential flows of an ideal fluid. The wave function is invariant with respect to the complex plane rotations group, and the asymptotics is constructed as a point-dependent action of this group on some function that is found by solving the transfer equation. It is shown in the paper, that if the Heisenberg group is used instead of the rotation group, then the limit of the equations solutions with ~ tending to zero leads to the equations for vortex flows of an ideal fluid in a potential field of forces. If the original Schrödinger equation is nonlinear, then equations for barotropic processes in an ideal fluid are obtained.

scholarly journals Kerr–Sen–Taub–NUT spacetime and circular geodesics

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Haryanto M. Siahaan
Keyword(s):  
String Theory ◽  
Equatorial Plane ◽  
Jacobi Equation ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Test Body ◽  
Low Energy ◽  
Energy Limit ◽  
Heterotic String Theory ◽  
Hamilton Jacobi Equation

AbstractWe present a solution obeying classical equation of motion in the low energy limit of heterotic string theory. The solution represents a rotating mass with electric charge and gravitomagnetic monopole moment. The corresponding conserved charges are discussed, and the separability of Hamilton–Jacobi equation for a test body in the spacetime is also investigated. Some numerical results related to the circular motions on equatorial plane are presented, but there is none that supports the existence of such geodesics.

Elementare Herleitung der Dirac-Gleichung / Elementary Derivation of the Dirac Equation

1978 ◽  
Vol 33 (11) ◽  
pp. 1378-1379 ◽  
Author(s):  
Hans Sallhofer
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Classical Equation ◽  
Inhomogeneous Media ◽  
Elementary Derivation ◽  
Complete Analogy

As is well known, the Schrödinger equation can be derived by suitably arranging the refraction in the classical equation for light inhomogeneous media. In this paper it is shown that one may derive the Dirac equation in complete analogy by arranging for the refraction in the electrodynamics of inhomogeneous media.

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