Related papers: Wave equations with energy dependent potentials
We review evolutionary models on quantum graphs expressed by linear and nonlinear partial differential equations. Existence and stability of the standing waves trapped on quantum graphs are studied by using methods of the variational…
The quantum dynamics generated by time-dependent variational calculations is discussed from the perspective of geometric quantization. On examples, it is shown that approximate energy eigenstates can be associated to the quantized periodic…
The aim of this note is to extend the energy decay estimates from [J. Wirth, J. Differential Equations 222 (2006) 487--514] to a broader class of time-dependent dissipation including very fast oscillations. This is achieved using…
We consider the problem of extracting physical predictions from the wave function of the universe in quantum cosmological models. We state the features of quantum cosmology an interpretational scheme should confront. We discuss the Everett…
The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which…
Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
The time-dependent electromagnetic field can results both pair waves and pair particles. It can be for mathematical relations between two functions with identical argument and difference of phases equal to $\pi$. Two examples both the…
A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result,…
We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
An effective operational approach to quantum mechanics is to focus on the evolution of wave-packets, for which the wave-function can be seen in the semi-classical regime as representing a classical motion dressed with extra degrees of…
In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although complex numbers have proven sufficient to predict the results of existing experiments, there is no apparent theoretical reason to choose them…
We consider the conditions for the time dependent potential in which the energy of the Cauchy problem of Klein-Gordon type equation asymptotically behaves like the energy of the wave equation. The conclusion of this paper is that the…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…