27,979 research outputs found
Comment on the numerical solutions of a new coupled MKdV system (2008 Phys. Scr. 78 045008)
In this comment we point out some wrong statements in the paper by Inc and
Cavlak, Phys. Scr. 78 (2008) 04500
Application of the Asymptotic Iteration Method to a Perturbed Coulomb Model
We show that the asymptotic iteration method converges and yields accurate
energies for a perturbed Coulomb model. We also discuss alternative
perturbation approaches to that model.Comment: 9 pages, 2 figures, 1 tabl
Accurate calculation of resonances in multiple-well oscillators
Quantum--mechanical multiple--well oscillators exhibit curious complex
eigenvalues that resemble resonances in models with continuum spectra. We
discuss a method for the accurate calculation of their real and imaginary
parts
The confined hydrogen atom with a moving nucleus
We study the hydrogen atom confined to a spherical box with impenetrable
walls but, unlike earlier pedagogical articles on the subject, we assume that
the nucleus also moves. We obtain the ground-state energy approximately by
means of first--order perturbation theory and by a more accurate variational
approach. We show that it is greater than the one for the case in which the
nucleus is clamped at the center of the box. Present approach resembles the
well-known treatment of the helium atom with clamped nucleus
Simple one-dimensional quantum-mechanical model for a particle attached to a surface
We present a simple one-dimensional quantum-mechanical model for a particle
attached to a surface. We solve the Schr\"odinger equation in terms of Weber
functions and discuss the behavior of the eigenvalues and eigenfunctions. We
derive the virial theorem and other exact relationships as well as the
asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for
model parameters corresponding to H adsorbed on Pd(100) and also outline the
application of the Rayleigh-Ritz variational method
A family of complex potentials with real spectrum
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that
is invariant under the combined effects of parity and time reversal
transformation. Numerical investigation shows that for some values of the
potential parameters the hamiltonian operator supports real eigenvalues and
localized eigenfunctions. In contrast with other PT symmetric models, which
require special integration paths in the complex plane, our model is integrable
along a line parallel to the real axis.Comment: Six figures and four table
Resonances for symmetric two-barrier potentials
We describe a method for the accurate calculation of bound-state and
resonance energies for one-dimensional potentials. We calculate the shape
resonances for symmetric two-barrier potentials and compare them with those
coming from the Siegert approximation, the complex scaling method and the
box-stabilization method. A comparison of the Breit-Wigner profile and the
transmission coefficient about its maximum illustrates that the agreement is
better the sharper the resonance
The Geography of Non-formal Manifolds
We show that there exist non-formal compact oriented manifolds of dimension
and with first Betti number if and only if and
, or and . Moreover, we present explicit
examples for each one of these cases.Comment: 8 pages, one reference update
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