相关论文: A new approximation method for time-dependent prob…

A general treatment of the quantal time-dependent coupled oscillators in presence of the variable magnetic field is presented. The treatment is based on the use of an alternative canonical transformations, time-dependent unitary…

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…

Using a generalized transfer matrix method we exactly solve the Schr\"odinger equation in a time periodic potential, with discretized Euclidean space-time. The ground state wave function propagates in space and time with an oscillating…

We apply the principles discussed in an earlier paper to the construction of discrete time field theories. We derive the discrete time field equations of motion and Noether's theorem and apply them to the Schrodinger equation to illustrate…

A closed-form solution to the energy-based stochastic Schrodinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist…

Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the…

We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…

We present the construction of an exponentially accurate time-dependent Born-Oppenheimer approximation for molecular quantum mechanics. We study molecular systems whose electron masses are held fixed and whose nuclear masses are…

In recent decades a lot of research has been done on the numerical solution of the time-dependent Schr\"odinger equation. On the one hand, some of the proposed numerical methods do not need any kind of matrix inversion, but source terms…

We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…

We consider a class of models describing a quantum oscillator in interaction with an environment. We show that models of continuous spontaneous localization based on a stochastic Schr\"odinger equation can be derived as an approximation to…

We present a systematic method for dealing with time dependent quantum dynamics, based on the quantum brachistochrone and matrix mechanics. We derive the explicit time dependence of the Hamiltonian operator for a number of constrained…

We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…

We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…

In this paper we introduce the use of Sylvester's formula for systems with degenerate eigenvalues in relation to obtaining their analytical solutions. To appreciate the use we include two other forms of analytical solutions namely adiabatic…

The formulation of the eigenvalue problem for the Schr\"odinger equation is studied, for the numerical solution a new approach is applied. With the usual exponentially rising free-state asymptotical behavior, and also with a first order…

We obtain a time-dependent Schrodinger equation for the Friedmann - Robertson - Walker (FRW) model interacting with a homogeneous scalar matter field. We show that for this purpose it is necesary to include an additional action invariant…

The nonlinear Schr\"odinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power…

We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys.…

The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…