3,538 research outputs found
Unparticle inspired corrections to the Gravitational Quantum Well
We consider unparticle inspired corrections of the type
to the Newtonian potential in the context of the
gravitational quantum well. The new energy spectrum is computed and bounds on
the parameters of these corrections are obtained from the knowledge of the
energy eigenvalues of the gravitational quantum well as measured by the GRANIT
experiment.Comment: Revtex4 file, 4 pages, 2 figures and 1 table. Version to match the
one published at Physical Review
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
Orthogonal Polynomials from Hermitian Matrices
A unified theory of orthogonal polynomials of a discrete variable is
presented through the eigenvalue problem of hermitian matrices of finite or
infinite dimensions. It can be considered as a matrix version of exactly
solvable Schr\"odinger equations. The hermitian matrices (factorisable
Hamiltonians) are real symmetric tri-diagonal (Jacobi) matrices corresponding
to second order difference equations. By solving the eigenvalue problem in two
different ways, the duality relation of the eigenpolynomials and their dual
polynomials is explicitly established. Through the techniques of exact
Heisenberg operator solution and shape invariance, various quantities, the two
types of eigenvalues (the eigenvalues and the sinusoidal coordinates), the
coefficients of the three term recurrence, the normalisation measures and the
normalisation constants etc. are determined explicitly.Comment: 53 pages, no figures. Several sentences and a reference are added. To
be published in J. Math. Phy
Continuum and Symmetry-Conserving Effects in Drip-line Nuclei Using Finite-range Forces
We report the first calculations of nuclear properties near the drip-lines
using the spherical Hartree-Fock-Bogoliubov mean-field theory with a
finite-range force supplemented by continuum and particle number projection
effects. Calculations were carried out in a basis made of the eigenstates of a
Woods-Saxon potential computed in a box, thereby garanteeing that continuum
effects were properly taken into account. Projection of the self-consistent
solutions on good particle number was carried out after variation, and an
approximation of the variation after projection result was used. We give the
position of the drip-lines and examine neutron densities in neutron-rich
nuclei. We discuss the sensitivity of nuclear observables upon continuum and
particle-number restoration effects.Comment: 5 pages, 3 figures, Phys. Rev. C77, 011301(R) (2008
Effective mass in quasi two-dimensional systems
The effective mass of the quasiparticle excitations in quasi two-dimensional
systems is calculated analytically. It is shown that the effective mass
increases sharply when the density approaches the critical one of
metal-insulator transition. This suggests a Mott type of transition rather than
an Anderson like transition.Comment: 3 pages 3 figure
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
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
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
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.
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
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