相关论文: Hamilton-Jacobi Many-Worlds Theory and the Heisenb…

We propose a new picture, which we call the {\it moving picture}, in quantum mechanics. The Schr\"{o}dinger equation in this picture is derived and its solution is examined. We also investigate the close relationship between the moving…

We combine the ideas of Dirac's orthonormal representation, Everett's relative state, and 't Hooft's ontological basis to define the notion of a world for quantum mechanics. Mathematically, for a quantum system $\mathcal{Q}$ with an…

The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by…

Time-dependent Schroedinger equation represents the basis of any quantum-theoretical approach. The question concerning its proper content in comparison to the classical physics has not been, however, fully answered until now. It will be…

Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr\"odinger equation. It was recently shown that the shape…

We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…

Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter…

The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…

Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy UR are often considered to be hallmarks of quantum theory. Here, a simple derivation of these URs is presented based on a single classical inequality from…

Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…

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…

The Hamilton-Jacobi method is generalized, both, in classical and relativistic mechanics. The implications in quantum mechanics are considered in the case of Klein-Gordon equation. We find that the wave functions of Klein-Gordon theory can…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

In this paper we develop a Hamilton-Jacobi theory in the setting of almost Poisson manifolds. The theory extends the classical Hamilton-Jacobi theory and can be also applied to very general situations including nonholonomic mechanical…

The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…

Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a long-wavelength approximation. We examine the non-linear evolution of the inhomogeneities in the dust fluid case and the cosmological constant case. In the case of dust…

We discuss the relation between the canonical Hamilton-Jacobi theory and the De Donder-Weyl Hamilton-Jacobi theory known in the calculus of variations using the examples of a scalar field in curved space-time and general relativity. By…

By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…

The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…