Related papers: Time-dependent conserved operators for autonomous …
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…
We consider the scattering theory for discrete Schr\"odinger operators on $Z^d$ with long-range potentials. We prove the existence of modified wave operators constructed in terms of solutions of a Hamilton-Jacobi equation on the torus…
The complete solutions of the Schr\"odinger equation for a particle with time-dependent mass moving in a time-dependent linear potential are presented. One solution is based on the wave function of the plane wave, and the other is with the…
Recently, it is shown that the extended phase space formulation of quantum mechanics is a suitable technique for studying the quantum dissipative systems. Here, as a further application of this formalism, we consider a dissipative system of…
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…
We show that, by using the quantum orthogonal functions invariant, we are able to solve a coupled of time dependent harmonic oscillators where all the time dependent frequencies are arbitrary. We do so, by transforming the time dependent…
Hamiltonian operators are gauge dependent. For overcome this difficulty we reexamined the effect of a gauge transformation on Schr\"odinger and Dirac equations. We show that the gauge invariance of the operator…
Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well $V\left( x,t\right) =if\left(t\right) \left\vert x\right\vert$. The problem…
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type…
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…
We eliminate by KAM methods the time dependence in a class of linear differential equations in $\ell^2$ subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator $…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
An analytical approach to quantum mechanical wave packet dynamics of laser-driven particles is presented. The time-dependent Schroedinger equation is solved for an electron exposed to a linearly polarized plane wave of arbitrary shape. The…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator…
We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme…
The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case…
We consider a free particle in a de Sitter spacetime. We use a picture in which the analogs of the Schr\"odinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which…
We analyse stability of observability estimates for solutions to wave and Scr\" odinger equations subjected to additive perturbations. The paper generalises the recent averaged observability/control result by allowing for systems consisting…