منابع مشابه
Quantum Hamilton-Jacobi equation
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A formal perturbative solution of th...
متن کاملAn Overview of the Hamilton-jacobi Equation
This paper is a survey of the Hamilton-Jacobi partial differential equation. We begin with its origins in Hamilton’s formulation of classical mechanics. Next, we show how the equation can fail to have a proper solution. Setting this issue aside temporarily, we move to a problem of optimal control to show another area in which the equation arises naturally. In the final section, we present some ...
متن کاملHomogenization of the Hamilton-jacobi Equation
Since the celebrated work by Lions, Papanicolaou and Varadhan in 1980’s, there has been a considerable attention to the homogenization problem for Hamilton-Jacobi equation: roughly speaking, how to describe what macroscopic properties and aspects of this equation survive, once all of its local features are neglected (for example, by averaging over faster and faster oscillations). The interest i...
متن کاملResurgence in a Hamilton Jacobi Equation
We study the resurgent structure associated with a Hamilton Jacobi equation This equation is obtained as the inner equation when studying the separatrix splitting problem for a perturbed pendulum via complex matching We derive the Bridge equation which encompasses in nitely many resurgent relations satis ed by the formal solution and the other components of the formal integral
متن کاملNonholonomic Hamilton–jacobi Equation and Integrability
We discuss an extension of the Hamilton–Jacobi theory to nonholonomic mechanics with a particular interest in its application to exactly integrating the equations of motion. We give an intrinsic proof of a nonholonomic analogue of the Hamilton–Jacobi theorem. Our intrinsic proof clarifies the difference from the conventional Hamilton–Jacobi theory for unconstrained systems. The proof also helps...
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ژورنال
عنوان ژورنال: Scholarpedia
سال: 2010
ISSN: 1941-6016
DOI: 10.4249/scholarpedia.8330