A consistent scheme is proposed for quantizing the potential amplitude in the Schrödinger equation in the caseof negative energies (lying in the discrete-spectrum domain). The properties of the eigenfunctionsφν(r) and eigenvalues ανcorresponding to zero, small, and large absolute values of energy E < 0 are analyzed. Expansion in the set {φν(r)} is used todevelop a regular pertur...

This paper deals with two domain decomposition methods for two dimensional linear Schrödinger equation, the Schwarz waveform relaxation method and the domain decomposition in space method. After presenting the classical algorithms, we propose a new algorithm for the Schrödinger equation with constant potential and a preconditioned algorithm for the general Schrödinger equation. These algorithms...

We consider the functional Schrödinger equation for a self interacting scalar field in an expanding geometry. By performing a time dependent scale transformation on the argument of the field we derive a functional Schrödinger equation whose hamiltonian is time independent but involves a time-odd term associated to a constraint on the expansion current. We study the mean field approximation to t...

We consider the cubic defocusing Schrödinger equation in two space dimen15 sions and prove that if the initial data are in H1/2, then there exists a global solution in time. The proof combines the argument from [5] with some new correlation estimates 17 for the Schrödinger equation.

Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided...

In this paper we use the Wigner transform to study properties of solutions to the Schrödinger equation. In particular, we present an elementary proof of the time decay inequalities for the free particle and harmonic oscillator. Furthermore, we estimate certain localized integral quantities in phase space, involving the Wigner transform of solutions to the Schrödinger equation.

In this letter, we consider the Schrödinger equation for a well potential with varying width. We solve one dimensional Schrödinger equation subject to time-dependent boundary conditions for a spinless particle inside infinite potential well, both wall of which move opposite direction with different velocities υ1 and υ2, respectively. PACS numbers: 03.65.Ge Typeset using REVTEX