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.