Related papers: Time-dependent Schr\"odinger equation from the Ham…

This paper has been withdrawn by the author because it needs to be rewritten completely.

This paper has been withdrawn by the author. The central result is now included in quant-ph/0309056 (as in the journal publication!). An erratum on the Heisenberg perturbation series estimate is also included therein.

This paper has been withdrawn by the author due to some error in the result

In this paper, we present a microscopic derivation of the two-dimensional focusing cubic nonlinear Schr\"odinger equation starting from an interacting $N$-particle system of Bosons. The interaction potential we consider is given by…

We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a…

A variationally improved Sturmian approximation for solving time-independent Schr\"odinger equation is developed. This approximation is used to obtain the energy levels of a quartic anharmonic oscillator, a quartic potential, and a Gaussian…

The Schr\"odinger equation $i \partial_t^\rho u(x,t)-u_{xx}(x,t) = p(t)q(x) + f(x,t)$ ( $0<t\leq T, \, 0<\rho<1$), with the Riemann-Liouville derivative is considered. An inverse problem is investigated in which, along with $u(x,t)$, also a…

A nonlocal-in-time problem for the abstract Schr\"odinger equation is considered. By exploiting the linear nature of nonlocal condition we derive an exact representation of the solution operator under assumptions that the spectrum of…

We study solutions to the Cauchy problem for the linear and nonlinear Schroedinger equation with a quadratic Hamiltonian depending on time. For the linear case the evolution operator can be expressed as an integral operator with the…

This paper has been withdrawn.

This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.

This paper has been withdrawn

This paper has been withdrawn as it has been superseded by 0808.2697

This paper has been withdrawn by the author(s) in the light of several other works available and due to a misunderstanding in the authorships.

Three analytic solutions to the Schr\"{o}dinger equation for the time-dependent Landau-Zener Hamiltonian are presented. They correspond to specific finite-time driving paths in a bounded parameter space of a two-level system. Two of these…

This paper has been withdrawn by the author.

We present a numerical study of the time-dependent SN equations in 3 dimensions with 3 different kinds of symmetry: spherically symmetric, axially symmetric and translationally symmetric. We find that the solutions manifest the competing…

This paper has been withdrawn by the authors. This is due to the fact that it has been substantially revised. As a consequence title and aim of the contents

I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper…

Parasupersymmetry of the one dimensional time-dependent Schr\"odinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of…