Re: IS quantum mechanics a limit cycle theory??

Due to material of my question in "Is quantum mechanics a limit cycle
theory" , it seems that I should ask, in priori, for an example of a
classical hamiltonian H with a finite (but non zero) number of closed
orbits (of course it is impossible in 2 dim.) If it is impossible to
present an example of hamiltonian with a finite number of closed
orbits, so the quantum interpretation for this "number" would be
meaningless!


> hello
> let we have a classical hamiltonian H,and we quantize
> it.
> I want to learn some relations between the behavior
> of solutions of X_H(the classic hamiltonian vector
> field) and some operetor theoretic invariants of the
> quantum operatores.In particular a nice
> interprewtation of the number of closed orbits of X_H
> in quantum language!
> Thank you for your suggestions for some deep
> references
> Ali Taghavi
>
> > Hi
> > I Am Intersted in the Hilbert 16th problem which
> main
> > object is "Limit
> > Cycle"!
> > Last Year I Found in the web a paper by Cetto and
> De
> > La Penna :with
> > The Title "Is Quantum Mechanics A Limit Cycle
> > Theory?"
> > this paper is available in Mathscinet.
> > I Invite you to review this paper and discuss on a
> > possible relation
> > between Hilbert 16th Problem And Mathematical
> Aspect
> > Of QM,
> > for begining:Let We Have A Planner Vector field
> > L(Lienard Equation )
> > as follow:
> > x'=y-F(x) y'=-x where F is A non even_polynomial
> ,we
> > are intersted in
> > the number of Limit Cycles Of L,consider the
> > following two
> > questions:(Assume F'(0) is not zero)
> > 1)Does there exist a correspondence between {closed
> > orbites} of L and
> > {closed orbits} of 4 dimensional (classical)
> > Hamiltonian (y-F(x))z-xw?
> > please see also the similar question in :
> >
> > http://www.arxiv.org/abs/math.CA/0409594
> >
> > 2)Let's Quantize the above 4 dimensional
> > hamiltonian:x,y stand for
> > operators multiplication by x and y,while z,w stand
> > for partial
> > derivative with respect to x ,y resp.
> > What Is The Quantum interpretations for (the number
> > of) closed orbits
> > of classical Hamiltonian
> > (y-F(x))z-xw?
> > Thank you
> > Ali Taghavi
> > Iran
> >
>

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