相关论文: A practice problem for Schr{\"o}dinger transmissio…
Rapidly convergent expansions of a one-loop contribution to the partition function of quantum fields with ellipsoid constant-energy surface dispersion law are derived. The omega-potential is naturally decomposed into three parts: the…
The envelope theory is a reliable and easy to implement method to solve time independent Schr\"odinger-like equations (eigenvalues and eigenvectors). It is particularly useful to solve many-body systems since the computational cost is…
The transfer matrix ${\mathbf{M}}$ of a short-range potential may be expressed in terms of the time-evolution operator for an effective two-level quantum system with a time-dependent non-Hermitian Hamiltonian. This leads to a dynamical…
Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d odd larger than 2. Here V is a bounded real- or complex-valued function vanishing outside the closed ball of center 0 and radius a. If V belongs to the class of potentials…
In this paper we suggest a natural interpretation of the de Broglie-Bohm quantum potential, as the energy due to the oscillating electromagnetic field (virtual photon) coupled with moving charged particle. Generalization of the…
A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…
Two drift-diffusion models for the quantum transport of electrons in graphene, which account for the spin degree of freedom, are derived from a spinorial Wigner equation with relaxation-time or mass- and spin-conserving matrix collision…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
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…
This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…
We investigate the dispersive properties of solutions to the Schr\"odinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schr\"odinger flow on…
After introducing the formalism of the general space and time fractional Schr\"odinger equation, we concentrate on the time fractional Schr\"odinger equation and present new results via the elegant language of Fox's H-functions. We show…
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…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
This paper is concerned with an inverse random potential problem for the Schr\"odinger equation. The random potential is assumed to be a generalized Gaussian random function, whose covariance operator is a classical pseudo-differential…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…
We study various direct and inverse spectral problems for the one-dimensional Schr\"{o}dinger equation with distributional potential and boundary conditions containing the eigenvalue parameter.
We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…
It is shown that the transmission line technology can be suitably used for simulating quantum mechanics. Using manageable and at the same time non-expensive technology, several quantum mechanical problems can be simulated for significant…