Existence of the time evolution for Schrödinger operators with time dependent singular potentials
Ulrich Wüller (1986)
Annales de l'I.H.P. Physique théorique
Kudryashov, Vladimir V., Vanne, Yulian V. (2002)
Journal of Applied Mathematics
Kime, K. (2000)
Electronic Journal of Differential Equations (EJDE) [electronic only]
David A. Mazziotti (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in...
Mazharimousavi, S.Habib, Mustafa, Omar (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Swanhild Bernstein (1996)
Banach Center Publications
We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces and . Further, we consider the Cauchy problem for this operator.
Jung, Wolf (2005)
Mathematical Physics Electronic Journal [electronic only]
Brandt, Achi (2000)
ETNA. Electronic Transactions on Numerical Analysis [electronic only]
Aleksander Ushveridze (1996)
Banach Center Publications
The systems of differential equations whose solutions exactly coincide with Bethe ansatz solutions for generalized Gaudin models are constructed. These equations are called the generalized spectral Riccati equations, because the simplest equation of this class has a standard Riccatian form. The general form of these equations is , i=1,..., r, where denote some homogeneous polynomials of degrees constructed from functional variables and their derivatives. It is assumed that . The problem...
Hussin, Véronique, Marquette, Ian (2011)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Komech, Alexander I., Komech, Andrew A. (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Bachelot, Alain (1989)
Portugaliae mathematica
Antonio Ambrosetti, Veronica Felli, Andrea Malchiodi (2005)
Journal of the European Mathematical Society
We deal with a class on nonlinear Schrödinger equations (NLS) with potentials , , and , . Working in weighted Sobolev spaces, the existence of ground states belonging to is proved under the assumption that for some . Furthermore, it is shown that are spikes concentrating at a minimum point of , where .
Kovalchuk, Vasyl, Slawianowski, Jan Jerzy (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Valenti, Davide (2009)
International Journal of Mathematics and Mathematical Sciences
Ruijsenaars, Simon N.M. (2009)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Gregory B. White (1993)
Annales de l'I.H.P. Physique théorique
Markus Bachmayr (2012)
ESAIM: Mathematical Modelling and Numerical Analysis
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....
Markus Bachmayr (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Markus Bachmayr (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...