We study in a systematic way all static solutions of the Goldstone model in 1+1 dimension with a periodicity condition imposed on the spatial coordinate. The solutions are presented in terms of the standard trigonometric functions and of Jacobi elliptic functions. Their stability analysis is carried out, and the complete list of classically stable quasi-topological solitons is given.

Virial relations for the Dirac equation in a central field and their applications to calculations of H-like atoms are considered. It is demonstrated that using these relations allows one to evaluate various average values for a hydrogenlike atom. The corresponding relations for non-diagonal matrix elements provide an effective method for analytical evaluations of infinite sums that occur in cal...