Related papers: Classical solution of the wave equation
A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…
In this papper, a quantum dynamical model describing the quantum measurement process is presented as an extensive generalization of the Coleman-Hepp model. In both the classical limit with very large quantum number and macroscopic limit…
While ultimately they are described by quantum mechanics, macroscopic mechanical systems are nevertheless observed to follow the trajectories predicted by classical mechanics. Hence, in the regime defining macroscopic physics, the…
A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…
An explicit expression for the finite-volume energy shift of shallow three-body bound states for non-identical particles is obtained in the unitary limit. The inclusion of the higher partial waves is considered. To this end, the method of…
We consider the Cauchy problem with smooth and compactly supported initial data for the wave equation in a general class of spherically symmetric geometries which are globally smooth and asymptotically flat. Under certain mild conditions on…
A simple, general discussion of the problem of inertia is provided both in classical physics and in the quantum world. After briefly reviewing the classical principles of equivalence (weak (WEP), Einstein (EEP), strong (SEP)), I pass to a…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
We argue that the main reason of crisis in quantum theory is that nature, which is fundamentally discrete and even finite, is described by classical mathematics involving the notions of infinitely small, continuity etc. Moreover, since…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
First, we show that there exists in classical mechanics three actions corresponding to different boundary conditions: two well-known actions, the Euler-Lagrange classical action S_cl(x,t;x_0), which links the initial position x_0 and its…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
In this work we consider an energy subcritical semi-linear wave equation ($3 < p < 5$) \[ \partial_t^2 u - \Delta u = \phi(x) |u|^{p-1} u, \qquad (x,t) \in {\mathbb R}^3 \times {\mathbb R} \] with initial data $(u,u_t)|_{t=0} = (u_0,u_1)\in…
A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the…
We study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution $F_\varepsilon=\mu +\varepsilon \sqrt{\mu}f_\varepsilon$ to the rescaled Boltzmann equation in the acoustic time scaling…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
The classical behaviour of a macroscopic system consisting of a large number of microscopic systems is derived in the framework of the Bohmian interpretation of quantum mechanics. Under appropriate assumptions concerning the localization…
In this paper we obtain the wave equation modeling the nematic liquid-crystals in three space dimensions and study the lifespan of classical solution to Cauchy problem. The almost global existence to classical solution for small initial…
In this paper, we mainly consider large time behavior for the classical free wave equation $u_{tt}-\Delta u=0$ in $\mathbb{R}^n$. We derive some large time optimal estimates for the quantity of solution $\|u(t,\cdot)\|_{L^2}$ with initial…
The physics of many closed, conservative systems can be described by both classical and quantum theories. The dynamics according to classical theory is symplectic and admits linear instabilities which would initially seem at odds with a…