Comment on `Solution of the Dirac equation for the Woods-Saxon potential with spin and pseudospin symmetry' [J. Y. Guo and Z-Q. Sheng, Phys. Lett. A 338 (2005) 90]

Out of the four bound-state solutions presented in loc. cit., only one (viz., the spin-symmetric one, in the low-mass regime) is shown compatible with the physical boundary conditions. We clarify the problem, correct the method and offer another, "missing" (viz., pseudospin-symmetric) new solution with certain counterintuitive "repulsion-generated" property.Comment: 6 p

Bound state equivalent potentials with the Lagrange mesh method

The Lagrange mesh method is a very simple procedure to accurately solve eigenvalue problems starting from a given nonrelativistic or semirelativistic two-body Hamiltonian with local or nonlocal potential. We show in this work that it can be applied to solve the inverse problem, namely, to find the equivalent local potential starting from a particular bound state wave function and the corresponding energy. In order to check the method, we apply it to several cases which are analytically solvable: the nonrelativistic harmonic oscillator and Coulomb potential, the nonlocal Yamaguchi potential and the semirelativistic harmonic oscillator. The potential is accurately computed in each case. In particular, our procedure deals efficiently with both nonrelativistic and semirelativistic kinematics.Comment: 6 figure

Absorption in atomic wires

The transfer matrix formalism is implemented in the form of the multiple collision technique to account for dissipative transmission processes by using complex potentials in several models of atomic chains. The absorption term is rigorously treated to recover unitarity for the non-hermitian hamiltonians. In contrast to other models of parametrized scatterers we assemble explicit potentials profiles in the form of delta arrays, Poschl-Teller holes and complex Scarf potentials. The techniques developed provide analytical expressions for the scattering and absorption probabilities of arbitrarily long wires. The approach presented is suitable for modelling molecular aggregate potentials and also supports new models of continuous disordered systems. The results obtained also suggest the possibility of using these complex potentials within disordered wires to study the loss of coherence in the electronic localization regime due to phase-breaking inelastic processes.Comment: 14 pages, 15 figures. To appear in Phys. Rev.

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength

Semirelativistic Hamiltonians and the auxiliary field method

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma\sqrt{\bm p^{2}+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schr\"odinger equation. Various shapes for the potential $V(r)$ are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail

Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method

For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained for a number of diatomic molecules and the results are compared with the findings of the super-symmetry, the hypervirial perturbation, the Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of Physics A: Mathematical and Genera

The Energy Eigenvalues of the Two Dimensional Hydrogen Atom in a Magnetic Field

In this paper, the energy eigenvalues of the two dimensional hydrogen atom are presented for the arbitrary Larmor frequencies by using the asymptotic iteration method. We first show the energy eigenvalues for the no magnetic field case analytically, and then we obtain the energy eigenvalues for the strong and weak magnetic field cases within an iterative approach for $n=2-10$ and $m=0-1$ states for several different arbitrary Larmor frequencies. The effect of the magnetic field on the energy eigenvalues is determined precisely. The results are in excellent agreement with the findings of the other methods and our method works for the cases where the others fail.Comment: 13 pages and 5 table

Any l-state solutions of the Woods-Saxon potential in arbitrary dimensions within the new improved quantization rule

The approximated energy eigenvalues and the corresponding eigenfunctions of the spherical Woods-Saxon effective potential in $D$ dimensions are obtained within the new improved quantization rule for all $l$-states. The Pekeris approximation is used to deal with the centrifugal term in the effective Woods-Saxon potential. The inter-dimensional degeneracies for various orbital quantum number $l$ and dimensional space $D$ are studied. The solutions for the Hulth\'{e}n potential, the three-dimensional (D=3), the $$-wave ($l=0$) and the cases are briefly discussed.Comment: 15 page

On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background

The problem of spin-0 and spin-1 bosons in the background of a general mixing of minimal and nonminimal vector inversely linear potentials is explored in a unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality criterion is set up and it is used to determine uniquely the set of solutions as well as to show that even-parity solutions do not exist.Comment: 10 page

BCS-BEC Crossover in Atomic Fermi Gases with a Narrow Resonance

We determine the effects on the BCS-BEC crossover of the energy dependence of the effective two-body interaction, which at low energies is determined by the effective range. To describe interactions with an effective range of either sign, we consider a single-channel model with a two-body interaction having an attractive square well and a repulsive square barrier. We investigate the two-body scattering properties of the model, and then solve the Eagles-Leggett equations for the zero temperature crossover, determining the momentum dependent gap and the chemical potential self-consistently. From this we investigate the dependence of the crossover on the effective range of the interaction.Comment: 12 pages, 14 figure