69,975 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
Accurate calculation of the complex eigenvalues of the Schr\"{o}dinger equation with an exponential potential
We show that the Riccati--Pad\'{e} method is suitable for the calculation of
the complex eigenvalues of the Schr\"{o}dinger equation with a repulsive
exponential potential. The accuracy of the results is remarkable for realistic
potential parameters
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
Formality of Donaldson submanifolds
We introduce the concept of s-formal minimal model as an extension of
formality. We prove that any orientable compact manifold M, of dimension 2n or
(2n-1), is formal if and only if M is (n-1)-formal. The formality and the hard
Lefschetz property are studied for the symplectic manifolds constructed by
Donaldson with asymptotically holomorphic techniques. This study permits us to
show an example of a Donaldson symplectic manifold of dimension eight which is
formal simply connected and does not satisfy the hard Lefschetz theorem.Comment: 24 pages, no figures, Latex2e; v3. statement of Lemma 2.7 correcte
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
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
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