Quantum Intuition

Fri, 17 May 1996 01:03:18 -0700 (PDT)
From: Zakhariev Boris Nikolaevich <zakharev@thsun1.jinr.dubna.su>
To: quantum-d@teleport.com
Subject: quantum intuition

Dear Colleagues,

  I am very interested in exchange of information concerning quantum
physics for education.

  Our publishing department has just printed my last book
(about new situation in quantum mechanics due to recnt success)
"Lessons on Quantum Intuition" with subtitles:
Gallery of wonderful potentials
Algorithms of spectral, scattering and decay management
Exactly solvable models of inverse problem and supersymmetry
Universal building elements -- "bricks and blocks" of quantum systems

  It is some kind of picture book; see also some review articles
(Phys.Elem.Part.&Nuclei 1990, N4; 1992, N5; 1994,N6) and original
publications  (Phys. Rev.A recent years) about new "elements of
quantum literacy" which we have understood  using the complete sets
of exactly solvable models and PC program "Mathematica". I also organize
every year a school-seminar "Secrets of quantum and mathematical
intuition" at Dubna.

  It is a proper moment now when an opportunity appeared to
give a simple explanation of what was till the recent time in
the black box of quantum puzzles.

  Inverse problem (IP) was developed with a big delay mainly by
mathematicians who were satisfied by the proof of the existence
theorems etc. It became clear however that physicists should themselves
develop their IP-intuition. In particular, by analyzing (the best of
thousands of) "inverse problem pictures" we can get a deeper insight
into the laws of the microworld and acquire the ability to make
qualitative predictions without computers and formulae (it is also
important for different applications to lift the understanding of
the wave mechanics on the intuitive level).

  Maybe it will be possible to combine yours and our experience in
improving the quality of quantum education.

  I would be glad to deliver a lecture(s) (seminar talk) about the new
achievements in quantum theory in your Institute on my way to colleagues
(specialists in inverse problem and supersymmetry) if I succeed in
organizing my trip to USA next year.

             Sincerely yours,
                               prof. B.N.Zakhariev.


   Some references

[1] Zakhariev B.N., Suzko A.A., Direct and Inverse
    Problems, (Chapter 2 !!) Springer-Verlag, Heidelberg, 1990.
[2] Zakhariev B.N. et al., Phys.Elem. Part.&Nuclei (Sov.J.Part.& Nucl.) 23
    N5 (1992) 603; ibid 21, N4 (1990), ibid 25, N6; Phys.Rev.A52, 3389
    1995; A46, 58, 1992; ibid A47, 3518, 1993; ibid A49, N5, 3159, 1994;
    ibid 50, N4, 1994; Phys.Lett.B319, 13, 1993; ibid 185, 265, 1987;
    Inverse Problems 3, 125, 1987.


 PS  The first breakthrough in our qualitative IP-feeling was
the understanding of the algorithms of variation of arbitrary
chosen bound state and scattering parameters  (they uniquely
determine the quantum system). Now it is possible to explain
concisely every detail of a potential shape transformation by
rearrangement of energy spectra and space localization of eigenstates,
to extract the fundamental constituents of these transformations
(to "split" them into elementary "bricks").
 It seems to be utterly important to have a complete set of these
universal elements to design a potential with desired quantum
properties.  That will help the broad community of physicists
to understand better the peculiarities of the quantum world.
So, we can predict the shape details of the potential transformations
which shift only the chosen energy level or to change the location
of a given bound state.
 Now we have achieved a new degree of clarity about the states
of continuous spectrum (arbitrary variation of resonance parameters)
and have got the qualitative connection of these notions with the
algorithms of removing and creating stationary energy levels,
"gathering" scattering states into bound states, absolute transparency
of potential barriers and "paradoxes" of wave motion over the lattices
(periodic structures, in space of discrete quantum numbers of mixed
configurations and channels etc).