Effects of a mixed vector-scalar kink-like potential for spinless particles in two-dimensional spacetime

The intrinsically relativistic problem of spinless particles subject to a general mixing of vector and scalar kink-like potentials ($\sim \mathrm{tanh} ,\gamma x$) is investigated. The problem is mapped into the exactly solvable Surm-Liouville problem with the Rosen-Morse potential and exact bounded solutions for particles and antiparticles are found. The behaviour of the spectrum is discussed in some detail. An apparent paradox concerning the uncertainty principle is solved by recurring to the concept of effective Compton wavelength.Comment: 13 pages, 4 figure

Spin and Pseudospin symmetries in the Dirac equation with central Coulomb potentials

We analyze in detail the analytical solutions of the Dirac equation with scalar S and vector V Coulomb radial potentials near the limit of spin and pseudospin symmetries, i.e., when those potentials have the same magnitude and either the same sign or opposite signs, respectively. By performing an expansion of the relevant coefficients we also assess the perturbative nature of both symmetries and their relations the (pseudo)spin-orbit coupling. The former analysis is made for both positive and negative energy solutions and we reproduce the relations between spin and pseudospin symmetries found before for nuclear mean-field potentials. We discuss the node structure of the radial functions and the quantum numbers of the solutions when there is spin or pseudospin symmetry, which we find to be similar to the well-known solutions of hydrogenic atoms.Comment: 9 pages, 2 figures, uses revte

The influence of statistical properties of Fourier coefficients on random surfaces

Many examples of natural systems can be described by random Gaussian surfaces. Much can be learned by analyzing the Fourier expansion of the surfaces, from which it is possible to determine the corresponding Hurst exponent and consequently establish the presence of scale invariance. We show that this symmetry is not affected by the distribution of the modulus of the Fourier coefficients. Furthermore, we investigate the role of the Fourier phases of random surfaces. In particular, we show how the surface is affected by a non-uniform distribution of phases

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.Comment: To appear in Eur. J. Phys. (5 pages