相关论文: Schrodinger Equation and Phase Space in Quantum Me…
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'.…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…
The major conceptual difficulties of quantum mechanics are analyzed. They are: the notion "wave-particle", the probabilistic interpretation of the Schroedinger wave \psi-function and hence the probability amplitude and its phase, long-range…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
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…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…