相关论文: Parameter differentiation and quantum state decomp…

We consider a two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We show that each component of the solutions to this system behaves like a free solution in the large time, but there is a strong…

The stationary Schroedinger equation of the harmonic oscillator is deformed by a Darboux transformation to construct time-dependent potentials with the oscillator profile. The Darboux (supersymmetric or factorization) method is usually…

We study the time evolution of a density matrix in a quantum mechanical system described by an ergodic magnetic Schr\"odinger operator with singular magnetic and electric potentials, the electric field being introduced adiabatically. We…

We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…

The commutators of the Poincar\'e group generators will be unchanged in form if a unitary transformation relates the free generators to the generators of an interacting relativistic theory. We test the concept of unitary transformations of…

In the Schroedinger picture, we find explicit solutions for two models of degenerate parametric oscillators in the case of multiparameter squeezed input photons. The corresponding photon statistics and Wigner's function are also derived in…

We use a Magnus approximation at the level of the equations of motion for a harmonic system with a time-dependent frequency, to find an expansion for its in-out effective action, and a unitary expansion for the Bogoliubov transformation…

In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…

In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…

We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…

We are dealing with possibly degenerate second-order parabolic operators whose coefficients are infinitely differentiable with respect to space variables and only measurable with respect to the time variable. We impose the H\"ormander…

We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…

A new class of time-energy uncertainty relations is directly derived from the Schr\"odinger equations for time-dependent Hamiltonians. Only the initial states and the Hamiltonians, but neither the instantaneous eigenstates nor the full…

A two-time quantum theory of a system of two particles with the direct electromagnetic interaction based on a quantum version of the action principle is considered. An analog of Schrodinger equation for the system is obtained.

In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…

Using closed positive extensions of the quadratic form in the potential term we provide alternative solutions to the eigenstate equation for the free quantum field Hamiltonian in the Schr\"o\-din\-ger representation. We show that admissible…

We review and compare different variational formulations for the Schr\"{o}dinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm…

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary…

In this note we address the exact solutions of a time-dependent Hamiltonian composed by an oscillator-like interaction with both a frequency and a mass term that depend on time. The latter is achieved by constructing the appropriate point…

In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…