Möbius transformations and monogenic functional calculus.
New method for computation of discrete spectrum of radical Schrödinger operator
A new method for computation of eigenvalues of the radial Schrödinger operator is presented. The potential is assumed to behave as if and as if . The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function . It is shown that the eigenvalues are the discontinuity points of the function . Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...
New representations of the Poincaré group describing two interacting bosons
Non-trapping condition for semiclassical Schrödinger operators with matrix-valued potentials.
Norm group convergence for singular Schrödinger operators
Note to the paper by R. Hempel, A. M. Hinz, and H. Kalf: On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.
Oč vlastně jde v teorii Schrodingerových operátorů?
On a theorem of Jörgens and Chernoff concerning essential self-adjointness of Dirac operators.
On diamagnetism and de Haas-van Alphen effect
On essential selfadjointness of the Weyl quantized relativistic Hamiltonian.
On higher order estimates in quantum electrodynamics.
On -accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry.
On -sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry
We consider a Schrödinger-type differential expression , where is a -bounded Hermitian connection on a Hermitian vector bundle of bounded geometry over a manifold of bounded geometry with metric and positive -bounded measure , and is a locally integrable section of the bundle of endomorphisms of . We give a sufficient condition for -sectoriality of a realization of in . In the proof we use generalized Kato’s inequality as well as a result on the positivity of satisfying the...
On phase segregation in nonlocal two-particle Hartree systems
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
On the Aharonov-Casher formula for different self-adjoint extensions of the Pauli operator with singular magnetic field.
On the asymptotic properties of quantum dynamics in the presence of a fractal spectrum
On the convergence of SCF algorithms for the Hartree-Fock equations
The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
On the essential spectrum of Dirac operators with spherically symmetric potentials.
On the essential spectrum of many-particle pseudorelativistic Hamiltonians with permutational symmetry account.
On the Essential Spectrum of Schrödinger Operators with Spherically Symmetric Potentials.