相关论文: Hamilton-Jacobi Many-Worlds Theory and the Heisenb…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
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…
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…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
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…
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…
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…
Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
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…
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…
We discuss two topics that are usually considered to be exclusively "quantum": the Schroedinger equation, and the uncertainty principle. We show (or rather recall) that the Schroedinger equation can be derived from Hamilton's equations…
Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty: Such a measure is…
In this article, we develop quantum mechanics upon the framework of the quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger point of view and the Hamilton-Jacobi point of view are fully equivalent in their…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
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…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined by a (Hamiltonian) constraint…