30 research outputs found
Two approximate formulae for the binding energies in Lambda hypernuclei and light nuclei
Two approximate formulae are given for the binding energies in
Lambda-hypernuclei and light nuclei by means of the (reduced) Poeschl-Teller
and the Gaussian central potentials. Those easily programmable formulae combine
the eigenvalues of the transformed Jacobi eigenequation and an application of
the hypervirial theorems.Comment: Accepted for publication in Europhysics Letter
Variational collocation for systems of coupled anharmonic oscillators
We have applied a collocation approach to obtain the numerical solution to
the stationary Schr\"odinger equation for systems of coupled oscillators. The
dependence of the discretized Hamiltonian on scale and angle parameters is
exploited to obtain optimal convergence to the exact results. A careful
comparison with results taken from the literature is performed, showing the
advantages of the present approach.Comment: 14 pages, 10 table
Application of the Frobenius method to the Schrodinger equation for a spherically symmetric potential: anharmonic oscillator
The power series method has been adapted to compute the spectrum of the
Schrodinger equation for central potential of the form . The bound-state energies
are given as zeros of a calculable function, if the potential is confined in a
spherical box. For an unconfined potential the interval bounding the energy
eigenvalues can be determined in a similar way with an arbitrarily chosen
precision. The very accurate results for various spherically symmetric
anharmonic potentials are presented.Comment: 16 pages, 5 figures, published in J. Phys
Study of a class of non-polynomial oscillator potentials
We develop a variational method to obtain accurate bounds for the
eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the
nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in
(-infinity,\infinity), g>0. The variational bounds are compared with results
previously obtained in the literature. An infinite set of exact solutions is
also obtained and used as a source of comparison eigenvalues.Comment: 16 page
Renormalization--Group Solutions for Yukawa Potential
The self--similar renormalization group is used to obtain expressions for the
spectrum of the Hamiltonian with the Yukawa potential. The critical screening
parameter above which there are no bound states is also obtained by this
method. The approach presented illustrates that one can achieve good accuracy
without involving extensive numerical calculations, but invoking instead the
renormalization--group techniques.Comment: 1 file, 12 pages, RevTe
Accurate energy spectrum for double-well potential: periodic basis
We present a variational study of employing the trigonometric basis functions
satisfying periodic boundary condition for the accurate calculation of
eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to
usual Dirichlet boundary condition, imposing periodic boundary condition on the
basis functions results in the existence of an inflection point with vanishing
curvature in the graph of the energy versus the domain of the variable. We show
that this boundary condition results in a higher accuracy in comparison to
Dirichlet boundary condition. This is due to the fact that the periodic basis
functions are not necessarily forced to vanish at the boundaries and can
properly fit themselves to the exact solutions.Comment: 15 pages, 5 figures, to appear in Molecular Physic
Eigenvalues from power--series expansions: an alternative approach
An appropriate rational approximation to the eigenfunction of the
Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the
eigenvalue accurately as the limit of a sequence of roots of Hankel
determinants. The convergence rate of this approach is greater than that for a
well--established method based on a power--series expansions weighted by a
Gaussian factor with an adjustable parameter (the so--called Hill--determinant
method)