Related papers: Time-dependent Schr\"odinger equation from the Ham…
We prove that if a solution of the discrete time-dependent Schr\"odinger equation with bounded real potential decays fast at two distinct times then the solution is trivial. For the free Shr\"odinger operator and for operators with…
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This paper has been withdrawn by the author(s)
For a time dependent Schr\"odinger equation, the scattering map is the map sending the asymptotic profile of solution as $t\to-\infty$ to its asymptotic profile as $t\to+\infty$. In this paper we show that, for certain class of metrics, the…
This paper has been removed by arXiv administrators because it overlaps gr-qc/0303009, hep-th/0405047, gr-qc/0412120, and others. This paper also has excessive overlap with the following papers also written by the authors or their…
We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band…
In this paper we discuss the relation between non-homogeneous nonlinear fractional diffusive equations and the Schrodinger equation with time-dependent harmonic potential. It is well known that the Cole-Hopf transformation allows to…
On the basis of the first principle -- the law of probability conservation and the Helmholtz decomposition theorem the authors have succeeded to construct the Schr\"odinger, Pauli, Dirac equation, the Hamilton-Jacobi equation and the…
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This paper has been withdrawn by the authors
This paper has been withdrawn.
We analyze the solutions of the Schr\"odinger equation with the low frequency initial data and a time-dependent weakly random potential. We prove a homogenization result for the low frequency component of the wave field. We also show that…
Using a variational approach based on a Lagrangian formulation and Gaussian trial functions, we derive a simple dynamical system that captures the main features of the time-dependent Schr\"odinger-Newton equations. With little analytical or…
This paper has been withdrawn
Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.
This paper has been withdrawn due to a crucial theoretical error.
This paper has been withdrawn.
This paper has been withdrawn.
This paper has been withdrawn by the authors.
This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.