Related papers: Time-dependent Schr\"odinger equation from the Ham…
This paper has been withdrawn by the author.
We present a microscopic derivation of the defocusing two-dimensional cubic nonlinear Schr\"odinger equation as a mean field equation starting from an interacting $N$-particle system of Bosons. We consider the interaction potential to be…
This paper has been withdrawn.
The paper has been withdrawn by the author.
The paper has been withdrawn.
The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.
The paper has been withdrawn
By substituting the diagonal and the other two adjacent diagonals terms with two different functions depending on two parameters of the discrete Laplacian operator, the nature of its spectrum changes from being purely continuous to…
In this paper we consider the nonlinear one-dimensional time-dependent Schroedinger equation with a periodic potential and a local perturbation. In the limit of large periodic potential the time behavior of the wavefunction can be…
This paper has been withdrawn by the author due to an error.
We discuss a new completely integrable case of the time-dependent Schroedinger equation in $R^n$ with variable coefficients for a modified oscillator, which is dual with respect to the time inversion to a model of the quantum oscillator…
This paper has been withdrawn by the author in favor of a stronger result proven by the author with R. Frank and T. Weidl in arXiv:0707.0998
This paper has been withdrawn by the author. The most updated version can be accessed by arXiv:1806.07290.
A method is proposed for extracting ionization amplitudes from the solution of the time-dependent Schr\"odinger equation (TDSE) describing a system in a time-dependent external field. The method is a hybrid of two earlier developed methods,…
This paper has been withdrawn, as all conjectures (and one claim) have been proven incorrect. Some of what remains may eventually reappear in a different context.
We present several results concerning the semiclassical limit of the time dependent Schr\"odinger equation with potentials whose regularity doesn't guarantee the uniqueness of the underlying classical flow. Different topologies for the…
This paper has been temporarily withdrawn for corrections.
We solve the Cauchy problem for the Schr\"odinger equation corresponding to the family of Hamiltonians $H_{\gamma(t)}$ in $L^{2}(\mathbb{R})$ which describes a $\delta'$-interaction with time-dependent strength $1/\gamma(t)$. We prove that…
This paper has been withdrawn by the author.
The paper was withdrawn by the authors.