相关论文: Wave equations with energy dependent potentials
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
We consider wave models with lower order terms and recollect some recent results on energy and dispersive estimates for their solution based on symbolic type estimates for coefficients and partly stabilisation conditions. The exposition is…
Energy decay is established for the damped wave equation on compact Riemannian manifolds where the damping coefficient is allowed to depend on time. Using a time dependent observability inequality, it is shown that the energy of solutions…
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…
Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
We discuss the concept of energy packets in respect to the energy transported by electromagnetic waves and we demonstrate that this physical quantity can be used in physical problems involving relativistic effects. This refined concept…
Quantum experiments detect particles, but they reveal information about wave properties. No matter how quanta are detected, they always express the local net state of the corresponding wave-function. The mechanism behind this process is…
We construct energy-dependent potentials for which the Schroedinger equations admit solu- tions in terms of exceptional orthogonal polynomials. Our method of construction is based on certain point transformations, applied to the equations…
We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.
We assume that particles are point-like objects even when not observed. We report on the consequences of our assumption within the realm of quantum theory. An important consequence is the necessity of vacuum fields to account for particle…
Using the time-dependent theory of quantum mechanics, we investigate nuclear electric dipole responses. The time evolution of a wave function is explicitly calculated in the coordinate-space representation. The particle continuum is treated…
In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
This article may be seen as a summary and a final discussion of the work that the author has done in recent years on the foundation of quantum theory. It is shown that quantum mechanics as a model follows under certain specific conditions…
In this paper we discuss the quantum potential approach of Bohm in the context of quantum cosmological model. This approach makes it possible to convert the wavefunction of the universe to a set of equations describing the time evolution of…
An assessment is given as to the extent to which pure unitary evolution, as distinct from environmental decohering interaction, can provide the transition necessary for an observer to interpret perceived quantum dynamics as classical. This…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…