相关论文: Wave functions of linear systems

In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.

It is shown that it is possible to construct the quantum wave functions for non-separable but integrable two-dimensional Hamiltonian systems, by solving suitable Dirichlet boundary values problems inside and outside the regions spanned by…

Wave guides for classical electromagnetic fields can realize the quantum evolution of the wave function for a system of qubits. Phase shifts, switches and beam splits allow for the construction of arbitrary quantum gates. They can act at…

In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…

An improved criterion for distinguishing conditions in which classical or quantum behavior occurs is developed by comparing classical and quantum mechanical measures of size while incorporating spatial and temporal restrictions on wave…

A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…

This paper focuses on a constructive treatment of the mathematical formalism of quantum theory and a possible role of constructivist philosophy in resolving the foundational problems of quantum mechanics, particularly, the controversy over…

We present a canonical way of assigning to each magnitude of a classical mechanical system a differential operator in the configuration space, thus rigorously establishing the Correspondence Principle for such systems. Here we show how each…

Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…

We develop the continuum mechanics of quantum many-body systems in the linear response regime. The basic variable of the theory is the displacement field, for which we derive a closed equation of motion under the assumption that the…

The dynamics of a quantum particle is governed by its wavefunction, which in turn is determined by the classical potential to which it is subjected. However the wavefunction itself induces a quantum potential, the particle `sees' the sum of…

A basic linearity of quantum dynamics, that density matrices are mapped linearly to density matrices, is proved very simply for a system that does not interact with anything else. It is assumed that at each time the physical quantities and…

Stunning progresses in the experimental resolution and control of natural or man-made complex systems at the level of their quantum mechanical constituents raises the question, across diverse subdisciplines of physics, chemistry and…

The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…

We introduce a concept of a quantum wide sense stationary process taking values in a C*-algebra and expected in a sub-algebra. The power spectrum of such a process is defined, in analogy to classical theory, as a positive measure on…

In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…

Various dualities are summarized. Based on the universal wave-particle duality, along an opposite direction of the developed quantum mechanics, we use a method where the wave quantities frequency and wave length are replaced on various…

The mathematical theory of quantum feedback networks has recently been developed for general open quantum dynamical systems interacting with bosonic input fields. In this article we show, for the special case of linear dynamical systems…

A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…

We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a…