Analytic structure of solutions to multiconfiguration equations (2008)
Fournais, Søren, Hoffmann-Ostenhof, Maria, Hoffmann-Ostenhof, Thomas, Sørensen, Thomas Østergaard
We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following:...
On spectral minimal partitions II, the case of the rectangle (2008)
Bonnaillie-Noël, Virginie, Helffer, Bernard, Hoffmann-Ostenhof, Thomas
In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-a/2,a/2[\times ]-b/2,b/2[\,$, with $0< a\leq b$. It has been observed in \cite{HHOT} that...
On spectral minimal partitions II, the case of the rectangle (2008)
Bonnaillie-Noël, Virginie, Helffer, Bernard, Hoffmann-Ostenhof, Thomas
In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-a/2,a/2[\times ]-b/2,b/2[\,$, with $0< a\leq b$. It has been observed in \cite{HHOT} that...
Analytic structure of many-body Coulombic wave functions (2008)
Fournais, Søren, Hoffmann-Ostenhof, Maria, Hoffmann-Ostenhof, Thomas, Sørensen, Thomas Østergaard
We investigate the analytic structure of solutions of non-relativistic Schr"odinger equations describing Coulombic many-particle systems. We prove the following: Let psi(x) with x=(x_1,...,x_N) in...
On spectral minimal partitions II, the case of the rectangle (2008)
Bonnaillie-Noël, Virginie, Helffer, Bernard, Hoffmann-Ostenhof, Thomas
In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-a/2,a/2[\times ]-b/2,b/2[\,$, with $0< a\leq b$. It has been observed in \cite{HHOT} that...
On spectral minimal partitions II, the case of the rectangle (2008)
Bonnaillie-Noël, Virginie, Helffer, Bernard, Hoffmann-Ostenhof, Thomas
In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-a/2,a/2[\times ]-b/2,b/2[\,$, with $0< a\leq b$. It has been observed in \cite{HHOT} that...
On spectral minimal partitions II, the case of the rectangle (2008)
Bonnaillie-Noël, Virginie, Helffer, Bernard, Hoffmann-Ostenhof, Thomas
In continuation of \cite{HHOT}, we discuss the question of spectral minimal 3-partitions for the rectangle $]-a/2,a/2[\times ]-b/2,b/2[\,$, with $0< a\leq b$. It has been observed in \cite{HHOT} that...
Electron wavefunctions and densities for atoms (2007)
Maria Hoffmann-ostenhof, Thomas Hoffmann-ostenhof, Stergaard Srensen
Abstract. With a special `Ansatz ' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, sup y2B(x;R) jr/(y)j...
Positivity and lower bounds to the decay of the atomic one-electron density (2006)
Fournais, Søren, Hoffmann-Ostenhof, Maria, Hoffmann-Ostenhof, Thomas, Sørensen, Thomas Østergaard
We investigate properties of the spherically averaged atomic one-electron density rho~(r). For a rho~ which stems from a physical ground state we prove that rho~ > 0. We also give exponentially...
Fournais, Søren, Hoffmann-Ostenhof, Maria, Hoffmann-Ostenhof, Thomas, Sørensen, Thomas Østergaard
We investigate regularity properties of molecular one-electron densities rho near the nuclei. In particular we derive a representation rho(x)=mu(x)*(e^F(x)) with an explicit function F, only...
Sharp regularity results for many-electron wave functions (2003)
Fournais, Søren, Hoffmann-Ostenhof, Maria, Hoffmann-Ostenhof, Thomas, Sørensen, Thomas Østergaard
We show that electronic wave functions Psi of atoms and molecules have a representation Psi=F*phi, where F is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and...
The Erwin, Schrödinger International Boltzmanngasse, Søren Fournais, Maria Hoffmann-ostenhof, Thomas Hoffmann-ostenhof, Thomas Østergaard Sørensen, ...
Abstract. We show that electronic wave functions ψ of atoms and molecules have a representation ψ = Fφ, where F is an explicit universal factor, locally Lipschitz, and independent of the...
THE ELECTRON DENSITY IS SMOOTH AWAY FROM THE NUCLEI (2001)
The Erwin, Schrödinger International Boltzmanngasse, Søren Fournais, Thomas Hoffmann-ostenhof, Thomas Østergaard Sørensen, Søren Fournais, ...
Abstract. We prove that the electron densities of electronic eigenfunctions of atoms and molecules are smooth away from the nuclei. 1. Introduction and Statement of the Results. We consider an...
Electron Wavefunctions and Densities for Atoms (2000)
Hoffmann-Ostenhof, Maria, Hoffmann-Ostenhof, Thomas, Sørensen, Thomas Østergaard
With a special `Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, $\sup_{y\in B(x,R)}|\nabla\psi(y)|...
Electron Wavefunctions and Densities for Atoms (2000)
The Erwin, Schrodinger International Boltzmanngasse, Thomas Hoffmann-Ostenhof, Thomas Hoffmann-ostenhof, Thomas Østergaard Sørensen
. With a special `Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, sup y2B(x;R) jr (y)j C(R) sup...
The Erwin, Schrödinger International Boltzmanngasse, Maria Hoffmann-ostenhof, Thomas Hoffmann-ostenhof, Thomas Østergaard Sørensen, Maria Hoffmann-ostenhof, ...
Abstract. With a special ‘Ansatz ’ we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, sup y∈B(x,R)...
Nodal Sets, Multiplicity and Superconductivity in Non Simply Connected Domains. (1999)
Bernard Helffer, Thomas Hoffmann-Ostenhof, Mark Owen
This is a survey on [HHOO] and further developments of the theory [He4]. We explain in detail the origin of the problem in superconductivity as first presented in [BeRu], recall the results of [HHOO]...
Bounds on the Multiplicity of Eigenvalues for Fixed Membranes (1998)
Thomas Hoffmann-Ostenhof, Peter W. Michor, Nikolai Nadirashvili
. For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k \Gamma 1. Here we prove that it is actually not greater than 2k \Gamma 3, for k 3. 1....
Ju Ly, Thomas Hoffmann-ostenhof, Peter W. Michor, Nikolai Nadirashvili
. For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k \Gamma 1. Here we prove that it is actually not greater than 2k \Gamma 3, for k 3. 1....
Bounds on the multiplicity of eigenvalues of fixed membrane (1998)
Thomas Hoffmann-ostenhof, Peter W. Michor, Nikolai Nadirashvili
Abstract. For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k − 1. Here we prove that it is actually not greater than 2k − 3, for k ≥ 3. 1....
Bounds on the multiplicity of eigenvalues of fixed membrane (1998)
Thomas Hoffmann-ostenhof, Peter W. Michor, Nikolai Nadirashvili
Abstract. For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k − 1. Here we prove that it is actually not greater than 2k − 3, for k ≥ 3. 1....
Bounds on the multiplicity of eigenvalues of fixed membrane (1998)
Thomas Hoffmann-ostenhof, Peter W. Michor, Nikolai Nadirashvili
Abstract. For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k − 1. Here we prove that it is actually not greater than 2k − 3, for k ≥ 3. 1....
Bounds on the Multiplicity of Eigenvalues for Fixed Membranes (1997)
The Erwin, Schrodinger International Boltzmanngasse, Thomas Hoffmann-Ostenhof, Thomas Hoffmann-ostenhof, Peter W. Michor, Peter W. Michor, ...
. For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k \Gamma 1. Here we prove that it is actually not greater than 2k \Gamma 3, for k 3. 1....