4,801 research outputs found
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 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 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 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
and 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 dimensions are obtained
within the new improved quantization rule for all -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 and dimensional space are studied. The solutions for the
Hulth\'{e}n potential, the three-dimensional (D=3), the -wave () 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
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