356 research outputs found
Some properties of WKB series
We investigate some properties of the WKB series for arbitrary analytic
potentials and then specifically for potentials ( even), where more
explicit formulae for the WKB terms are derived. Our main new results are: (i)
We find the explicit functional form for the general WKB terms ,
where one has only to solve a general recursion relation for the rational
coefficients. (ii) We give a systematic algorithm for a dramatic simplification
of the integrated WKB terms that enter the energy
eigenvalue equation. (iii) We derive almost explicit formulae for the WKB terms
for the energy eigenvalues of the homogeneous power law potentials , where is even. In particular, we obtain effective algorithms to
compute and reduce the terms of these series.Comment: 18 pages, submitted to Journal of Physics A: Mathematical and Genera
On the semiclassical expansion for 1-dim potentials
In the present paper we study the structure of the WKB series for the
polynomial potential ( even). In particular, we obtain relatively
simple recurrence formula of the coefficients \s'_k of the semiclassical
approximation and of the WKB terms for the energy eigenvalues.Comment: 5 pages, PTP LaTeX style, to be published in the proceedings of the
conference/summer school 'Let's Face Chaos through Nonlinear Dynamics',
Maribor, Slovenia, June/July 1999, eds. M. Robnik et al., Prog. Theor. Phys.
Suppl. (Kyoto) 139 (2000
Limit cycle bifurcations from a nilpotent focus or center of planar systems
In this paper, we study the analytical property of the Poincare return map
and the generalized focal values of an analytical planar system with a
nilpotent focus or center. Then we use the focal values and the map to study
the number of limit cycles of this kind of systems with parameters, and obtain
some new results on the lower and upper bounds of the maximal number of limit
cycles near the nilpotent focus or center.Comment: This paper was submitted to Journal of Mathematical Analysis and
Application
On the definition of equilibrium and non-equilibrium states in dynamical systems
We propose a definition of equilibrium and non-equilibrium states in
dynamical systems on the basis of the time average. We show numerically that
there exists a non-equilibrium non-stationary state in the coupled modified
Bernoulli map lattice.Comment: 4 pages, 2 figure
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