Related papers: A complex-linear reformulation of Hamilton-Jacobi …
I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schr\"odinger equation is just the classical H-J equation, constrained by a condition that…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear…
The Hamilton-Jacobi theory of Classical Mechanics can be extended in a novel manner to systems which are fuzzy in the sense that they can be represented by wave functions. A constructive interference of the phases of the wave functions then…
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…
The numerical version of the Hamilton-Jacobi quantization method, recently proposed, is applied to the one dimensional quartic oscillator. A suitable quantization condition is formulated and various energy levels and wave functions are…
The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the…
Hamilton-Jacobi theory is a fundamental subject of classical mechanics and has also an important role in the development of quantum mechanics. Its conceptual framework results from the advantages of transformation theory and, for this…
A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
For a general mechanical system, it is shown that each solution of the Hamilton-Jacobi equation defines an N=2 pseudo-supersymmetric extension of the system, such that the usual relation of the momenta to Hamilton's principal function is…
General analytical solutions of the Quantum Hamilton Jacobi Equation for conservative one-dimensional or reducible motion are presented and discussed. The quantum Hamilton's characteristic function and its derivative, i.e. the quantum…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
We review here some conventional as well as less conventional aspects of the time-independent and time-dependent Hamilton-Jacobi (HJ) theory and of its connections with Quantum Mechanics. Less conventional aspects involve the HJ theory on…
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms…
The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor)…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
Observables of quantum or classical mechanics form algebras called quantum or classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf 8}…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
A basic aspect of the recently proposed approach to quantum mechanics is that no use of any axiomatic interpretation of the wave function is made. In particular, the quantum potential turns out to be an intrinsic potential energy of the…