Numerical computation and analysis of the Titchmarsh–Weyl mα(λ) function for some simple potentials

AbstractThis article is concerned with the Titchmarsh–Weyl mα(λ) function for the differential equation d2y/dx2+[λ−q(x)]y=0. The test potential q(x)=x2, for which the relevant mα(λ) functions are meromorphic, having simple poles at the points λ=4k+1 and λ=4k+3, is studied in detail. We are able to calculate the mα(λ) function both far from and near to these poles. The calculation is then extended to several other potentials, some of which do not have analytical solutions. Numerical data are given for the Titchmarsh–Weyl mα(λ) function for these potentials to illustrate the computational effectiveness of the method used

On a representation of vector continued fractions.

Vector Pade approximants to power series with vector coefficients may be calculated using the three-term recurrence relations of vector continued fractionsif formulated in the framework of Clifford algebras. We show that the numerator and denominator polynomials of these fractions take particularly simple forms which require just a few degrees of freedom in their representation. The new description also allows the calculation of ”hybrid” approximants

A Hill-series approach to wavefunction nodes

International audienc

Adding a complex shift to HVPT

International audienc

The Schroedinger equation with position-dependent mass

International audienc

Direct calculation of off-diagonal matrix elements

International audienc

Off-diagonal matrix elements: a modus tollens approach

International audienc

Investigation of the interaction of some astrobiological molecules with the surface of a graphite (0001) substrate. Application to the CO, HCN, H2O and H2CO molecules

International audienceDetailed interaction potential energy calculations are performed to determine the potential energy surface experienced by the molecules CO, HCN, H2O and H2CO, when adsorbed on the basal plane (0 0 0 1) of graphite at low temperatures. The potential energy surface is used to find the equilibrium site and configuration of a molecule on the surface and its corresponding adsorption energy. The diffusion constant associated with molecular surface diffusion is calculated for each molecul