Propagating edge states for a magnetic Hamiltonian.
Propagation estimates for N-body Stark hamiltonians
Quadratic algebra approach to an exactly solvable position-dependent mass Schrödinger equation in two dimensions.
Quantum energy expectation in periodic time-dependent Hamiltonians via Green functions.
Quantum graph spectra of a graphyne structure
We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.
Quantum scattering near the lowest Landau threshold for a Schrödinger operator with a constant magnetic field
For fixed magnetic quantum number m results on spectral properties and scattering theory are given for the three-dimensional Schrödinger operator with a constant magnetic field and an axisymmetrical electric potential V. In various, mostly singular settings, asymptotic expansions for the resolvent of the Hamiltonian H m+Hom+V are deduced as the spectral parameter tends to the lowest Landau threshold. Furthermore, scattering theory for the pair (H m, H om) is established and asymptotic expansions...
Quasi-exactly solvable -body spin Hamiltonians with short-range interaction potentials.
Radiation conditions and resolvent estimates for relativistic Schrödinger operators
Rate of convergence for large coupling limits by brownian motion
Reducibility and point spectrum for linear quasi-periodic skew-products.
Regularity of the multi-configuration time-dependent Hartree approximation in quantum molecular dynamics
We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional nuclear wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained via the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of low-dimensional nonlinear partial differential...
Remark to the problem of eigenvalues of Schrödinger equation
Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients
We consider Schrödinger operators on with variable coefficients. Let be the free Schrödinger operator and we suppose is a “short-range” perturbation of . Then, under the nontrapping condition, we show that the time evolution operator: can be written as a product of the free evolution operator and a Fourier integral operator which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators. These results...
Revisiting the symmetries of the quantum Smorodinsky-Winternitz system in dimensions.
Riccati and Ermakov equations in time-dependent and time-independent quantum systems.
Self-similar solutions for nonlinear Schrödinger equations.
Semi-classical approximation and microcanonical ensemble
Semiclassical states for weakly coupled nonlinear Schrödinger systems
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
Short waves through thin interfaces and 2-microlocal measures
Singular integrals of the time-harmonic relativistic Dirac equation on a piecewise Liapunov surface.