Solving the Schroedinger equation for bound states with Mathematica 3.0

Using Mathematica 3.0, the Schroedinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically.Comment: LaTeX, 11 pages, 2 figures; minor change in program listin

Spinless Salpeter Equation: Some (Semi-) Analytical Approaches

Several techniques for deriving semianalytical bounds on the energy eigenvalues of the spinless Salpeter equation and for estimating the quality of the corresponding approximate eigenstates are reviewed

Numerical Solution of the Spinless Salpeter Equation by a Semianalytical Matrix Method (a Mathematica 4.0 routine)

In quantum theory, the so-called "spinless Salpeter equation," the relativistic generalization of the nonrelativistic Schroedinger equation, is used to describe both bound states of scalar particles and the spin-averaged spectra of bound states of fermions. A numerical procedure solves the spinless Salpeter equation by approximating this eigenvalue equation by a matrix eigenvalue problem with explicitly known matrices.Comment: 7 pages, LaTe

The Spinless Relativistic Woods-Saxon Problem

Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem posed by the spinless Salpeter equation and recall various elementary knowledge, considerations, and techniques that practitioners seeking solutions to this specific reduction of the Bethe-Salpeter equation may find helpful.Comment: 12 page

Instantaneous Bethe-Salpeter Look at the Lightest Pseudoscalar Mesons

Within our description of Goldstone-type pseudoscalar mesons as almost massless bound states of quark and antiquark by a three-dimensional bound-state equation of Bethe-Salpeter origin, taking into account the pointwise behaviour of the full light-quark propagators enables to characterize the effective interquark interactions more precisely than earlier studies exploiting just specific aspects.Comment: 4 pages, 2 figures, contributed to "XVII International Conference on Hadron Spectroscopy and Structure - Hadron2017" (25 - 29 September 2017, Salamanca, Spain