arXiv subjects

F. F. Schoberl

Publications and source records attributed to F. F. Schoberl.

22 records · Page 2Linked to original sources

arXiv1999

The One-Dimensional Spinless Relativistic Coulomb Problem

Motivated by a recent analysis which presents explicitly the general solution, we consider the eigenvalue problem of the spinless Salpeter equation with a ("hard-core amended") Coulomb potential in one dimension. We prove the existence of a critical coupling constant (which contradicts the assertions of the previous analysis) and give analytic upper bounds on the energy eigenvalues. These upper bounds seem to disprove the previous explicit solution.

hep-ph↗

arXiv1999

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.

hep-ph↗

arXiv1998

Bound States by the Spinless Salpeter Equation

In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy levels and wave functions. These theorems are applied to the prototype of all relativistic wave equations, the spinless Salpeter equation.

hep-ph↗

arXiv1998

Semirelativistic Treatment of Bound States

This talk reviews several aspects of the "semirelativistic" description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating relativistic effects) and, in particular, presents or recalls some very simple and elementary methods which allow to derive rigorous statements on the corresponding solutions, that is, on energy levels as well as wave functions. In principle, these methods work for all physical situations which may be formulated as an eigenvalue problem.

hep-ph↗