[Fis] Quantum Mechanics: Logic and Formalisms

[Fis] Quantum Mechanics: Logic and Formalisms

From: Julio Stern <[email protected]>
Date: Tue 06 Jun 2006 - 20:59:46 CEST

Dear friends, and specialists in the logic(s)
and formalism(s) of Quantum Mechanics:
(If you dont have an on line LaTeX compiler,
  please read the attached pdf file... )

Following von Foerster, I consider systemic eigen-solutions
as the most basic objects of knowledge.
Therefore, studying the essential properties and the process of
emergence of eigen-solutions in scientific research constitutes
(for me) the foundation of a true constructivist epistemology.

Once upon a time,
I stumble on a result stated in Nosov and Kolmanovskii (1986, p.13):

{\it ``In a recent paper Zubov has considered the problem of
relativistic particle motion in a central field. The equation
of motion of this particle is
\[
    m \ddot{r}(t) = -k
    \frac{r(t -\tau(r))}{|r(t -\tau(r))|^3} \ .
\]
Here $r$ is a vector joining the particle with the
immovable center. It is known that in such a system
without delay, i.e. for $\tau(r)=0$, a unique circular
orbit passes across every point $(x_0,y_0,z_0)$ of the
configuration space. If we allow for the interaction delay,
then the situation changes qualitatively. The circular orbits
settle on the spheres if and only if their radii verify the
quantization conditions
\[ \nu(|r|) \tau(|r|) = n 2\pi \ \ , \ \
    n= 0, \pm 1, \pm 2, \ldots
\]
(These) conditions coincide with Bohr quantization rules.''}

\r V.R.Nosov, V.B.Kolmanovskii (1986).
{\it Stability of Functional Diferential Equations.}
London: Academic Press.

\r V.I.Zubov (1983). {\it Analytical Dynamics of Systems of
  Bodies.} Leningrad University.

I found Zubov's result astonishingly beautyfull.
The eigen solutions of Bohr quantization rule where obtained
out of a spherical symmetry constraint, in the formalism
of functional (delay) differential equations.
This formalism was (for me) such more natural and intuitive
than Schr\"{o}dinger equation.
I spend some time trying to get more of the standard
eigen-solutions of QM out of this language.
My knowledge of delayed differential equations is very
limited, so I was not very successful.
I also never had access to Zubov's papers.

Do you know if this line of research had continuation?
Can any of you get me a copy of Zubov's paper(s)
from Leningrad University?

Thank you very much,
Julio Michael Stern.
jmstern@hotmail.com

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  • application/pdf attachment: zub.pdf
Received on Tue Jun 6 21:00:47 2006


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