Oč vlastně jde v teorii Schrodingerových operátorů?
Odd anharmonic oscillators and shape resonances
On a class of conservative, highly accurate Galerkin methods for the Schrödinger equation
On a differential equation approach to quantum field theory : causality property for the solutions of Thirring's model
On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the normal derivative of the groundstate on the boundary. We then propose to use this formulation in the...
On a q-deformed harmonic oscillator with variable linear momentum.
On a theorem of Jörgens and Chernoff concerning essential self-adjointness of Dirac operators.
On absorbing boundary conditions for quantum transport equations
On an example of phase-space tunneling
On coupling constant thresholds and related eigenvalue properties 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 nodal sets and nodal domains on and
We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on . We also construct a solution of the equation in that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.
On nonlinear Schrödinger equations in exterior domains
On orthogonality relations for dual discrete -ultraspherical polynomials.
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 quantum twist maps and spectral properties of Floquet operators