About my scientific chief Ya. A. Smorodinsky

About my scientific chief Ya. A. Smorodinsky
 
                Zakhariev B.N. (Lab. Theor. Phys. JINR, Dubna)

The  research physical contacts with Ya.A. , the  first scientific teacher of one of the present authors  (B.N.) were something paradoxical. During the whole period (about ten years when Z. belonged officially to the group of  Smorodinsky) there (do not)  appeared (no)  their common publications (as later it became clear the scientific  hints of principal importance were our guides through the whole our life..
One of the reasons of this situation was the feeling  shy of the young collaborator before the seemingly so highly authoritative  chief .It was  due to inability to understand clear enough the essence of the problems he suggested to solve and the simple fear to  confess the “shameful” unfamiliarity with many elementary facts forgotten  or omitted during the education at university. Now it seems evident that there was the guilt of both sides. The analogous situation appears to be later when  I  (B.Z.)   became a research advisor of  a younger Mongolian 
collaborator Lhagva in the laboratory of theoretical physics at JINR  (Dubna)  and tried to involve him into creative activity. The experience of my own mistakes and their comparison with the previous difficulties  of  understanding  Ya.A.  results in more careful (attentive) relations with less informed and to be more “brave” (no fear of  asking any “stupid” questions) with  supposedly those understanding the essence of the considered problems. So that  were some valuable lessons which  I have got from my teacher. Later it yield in composing my article [??] about some aspects (my own advises ?????) of how to overcome several obstacles in scientific search of new discoveries. I hope to rewrite this article improving it in the near future .

It is not excluded that the (complex) of self-distrust of Smorodinsky had some influence on me. I have mentioned not seldom that Ya.A. during his explanations began to erase what ha has just written on the black board being afraid that he has made an error (Landau “terror” …??)

Criteria of determination  of  our (my) ability to?? success, e.g.  in writing books and development of new theories were  of not too high quality.  I think Ya.A. was surprised  by my results. Being often against publication of our books, he later once recommended my “Lessons on quantum intuition” to Chinese professor visiting JINR  (it is a good book).

When I asked S. to hear about my new ideas he tried to discourage me from the very beginning? (disappoint?) me. I feel ? that this was not good for my future work on improvement of the idea. So I decided to  share the new ideas with chief only after I became more or less sure in them. Really, this gave the wanted result (was achieved). So I can suggest this to others…
But even in this case after five minutes  the face of S.  became boring. I think it was not the   evaluation of the quality of the idea, but simply that even success of  the young collaborator  was not important for S. (he did not expect  something very interesting from us already because we were not belonged to the wanted contingent of the selected manifold?.

The receipts which help to do discoveries may be useful also in our general behavior. I have not so quickly learned?? even after I understood that I nee not to be ashamed  when I want to express thanks, to praise somebody, to suggest the help to somebody.
For me it was instructive when I  mentioned in Germany an incident in tram. One passenger pushed (?) some other one. What was new for me that the both were as if very glad with what was  happened between them: because the considered this event as a good occasion to show their  respect to one another as two good citizens what made them more please gladful than before  the incident. For me it was good example how people can make free themselves of unnecessary and
hindering  restrictions.

Here and with Efros the victories above? ourselves  and liberation of our own weaknesses.
  The principal importance of the clear presentation of scientific results I think can be illustrated by Einstein opinion that if somebody understands somewhat, his explanation must be understandable for his grandmother. This was one of the causes of his success  in comparison with some of his (concurents) competitors . Really, the more  lower is the threshold of people to whom the subject could be clearly explained, the wider is the manifold of  people among whom the fame of the research results could be spread, the more popular became the author. So the efforts expended for improvement (simplification) of  the presentation can be compensated by the degree of  the coverage of the audience of the informed community. And besides this the experience of success in one case helps to achieve analogous result something like next time  with less efforts. So both the science and the author gain???

There is some obstacle in determination what is not understood, because for not enough informed it may be difficult to formulate it. But particularly this can be achieved through the series of control questions given by the more informed??? partner to the less informed one and the defects of knowledge so revealed could be corrected comparatively simple.

It has beside the negative side also positive sides. The unusual freedom although appeared due to time economy of Ya. A., but simultaneously promotes our selfdetermination?????????. This positive effect appears to be more strong. Such degree of  freedom has nobody (a seldom thing) in our institute.

(The important event of our interaction with Ya.A. was his rather seldom clear  formulation for me of the problem. It was the difficulty in generalizing the few body wave function  expansion in the complete set of hyper-spherical harmonics to the case of not localized  scattering states. At that time Simonov demonstrated their remarkable application to bound states.

The way out of this situation was found by us due to the fact that just the hindering scattering few-body asymptotic wave parts appeared to be much simpler due to the vanishing of some interactions at large distances. Then separating the whole wave into the main central part and partly free (simplified) waves at big distances allows the simplified  separate  treatment of both parts: the localized center in analogy with the description of bound states and the other part as the products of less particle fragments.

This appears to be a key approach to overcome the obstacles in description of nuclear reactions with rearrangement of particles. This was the generalization of the widely known  “unified theory of nuclear reactions” by H.Feshbach [??].

This appears to be a key approach to overcome the obstacles in description of nuclear reactions with rearrangement of particles. This was the generalization of the widely known  “unified theory of nuclear reactions” by H.Feshbach [??].

???The comparison with the formalism of exactly solvable models of  IP can create the suspicion that  there are some common aspects………?????????
  Unfortunately  we do not succeed in combination this approach with the  formalism of  inverse problem exactly solvable models (V.Ch . has found an error in such our  paper [??]).

Although there was lack of understanding between us and  Ya.A. he did not want to spend extra time for discussions with us and to search new tasks within our powers , but nevertheless some of his suggestions as perspective directions of research development were used by us, sometimes after  a long time (for example, the quantum inverse problem ).

????????????????
.V. Pustovalov Efros some problem of not exactly independent condition of thinking about the method (Smorodinsky informed V.V.  Pustovalov in Kurchatov Institute about our progress in investigation – our idea to subtract asymptotes  (following Levin) discovery identical particle – a step to the method of subtracted asymptotes.
But it was a good result : that we demonstrated the ability to overcome these psychological obstacles? And Ya.A. do not hinder us (do not interfere in our decision of the “conflict” of some our misunderstanding.
Later both Kurchatovs institute and JINR groups were seen that their new results clearly demonstrated the big progress ( high quality of  IP few body physics).               

Almost at the beginning of the creation of the IP theory  (integral equations of the quantum IP)  by Gelfand-Levitan-Marchenko   our chief  S. has drown our attention  to this remarkable event and suggested and suggested to perform some calculations in this direction? We with V.Belyaev have even sent a corresponding paper for publication. But soon  S. without discussion with us, being afraid  of critic from mathematicians. He at that time had some conversation with the classic of  IP, Boris Moiseevich Levitan who criticized Ya.A. strongly, so that our chief  decided
not to risk in near future to have a repetition  of analogous attacks. It was something common with smearing out from the blackboard what he had just written, but was not sure whether it was
not correct. Very probably he was right at that time. We ourselves at that time did not have a clear notion about IP.  But what was pity,  S. after that has not returned to IP. Ya.A. caused difficulties for publication of our first book on IP (this was described in our book [??]. And  when I asked him to recommend translation of R.Newtons book on 3 dimensional IP and publication it by the publishing house MIR where he was a member of Editorial Board, Ya.A. promised to do so, but did not accomplished it.   

Wonderfully for too long time we have not (been grasping?) grasped the essential side of the inverse problem : that it presents us infinite complete sets of one-dimensional exactly solvable models of elementary spectral transformations. But till now the great majority of the physical community is unaware of this. Maybe this happened because the inverse problem was suggested  by mathematicians as an ill posed problem. Here was important my visit to classic of IP  V.Marchenko at Kharkov  (Institute of low energies) who draw my attention to some aspects of this fact. Of course, V.M. could not foresee that we shall use his advise for creation a theory of qualitative quantum intuitive predictions : elementary bricks and blocks of wave and potential
Transformations which allow to predict immediately the results without computer (solutions “in Finally, following the advise of Marchenko during my visit to him ILT??? We turned our main attention to exactly solvable models  of IP. Although it required to much time, until we began to understand what originally we ourselves can contribute to the excellent formalism  of claasics. And may be mathematicians also do not clearly imagine what we need?? from IP. It became evident during the IP conference at lake Balaton (Hungary) were Levitan was surprised by our breakthrough in IP, what he expressed by the statement (“I like you”) after my report at the opening of the Conference after report of another classic Marchenko. Although just Levitan said me openly? after my praises of mathematicians that their opinions about physicists are not so advantageous.
Levitan said me once that he considered his results on IP  as far from the best ones among what he has done, although their fame was much more reverberating. I think that for him our results were quite unexpected that such simple rules can exist at all.
mind”).

\section{Systems of Schr\"odinger equations. Unexpected role of nondiagonal elements of interaction matrix in bending of partial
channel wave functions }

Generalized and instructive rules of bending multi-channel partial waves $\Psi _{\alpha }$ were recently found. They open the way to understand  multi-dimensional and many-body systems. The formalism of
vector functions with partial components $\Psi_{\alpha}(x) $ and matrix interaction $||V_{\alpha \beta }(x)||$ instead of scalar potential  $V(x)$ was considered by us in [1] 2000, see also references therein. For simplicity we shall consider here the two-channel case
\begin{eqnarray}
-\Psi"_{1}(x) =(E_{1}- V_{11}(x))\Psi_{1}(x) -V_{12}(x)\Psi_{2}(x) \nonumber \\
-\Psi"_{2}(x) =(E_{2}- V_{22}(x))\Psi_{2}(x)-V_{21}(x)\Psi_{1}(x),
 \label{system2}
\end{eqnarray}
where $E_{\alpha }=E-\epsilon_{\alpha }$ and  $\epsilon_{\alpha}$
are threshold values of continuous spectra  of different channels.
 The qualitative results here will be valid in principle for general system with  $ V_{\alpha \beta(x)}$  coupling of arbitrary $\alpha $  and $_\beta  $ channels.

\Subsection{Principal possibility of attractive potential barriers and repulsive wells}

We ourselves considered this as sensation.
 

That is true, the diagonal elements   $V_{\alpha \alpha }$  of {\it interaction matrix} influence on   $\Psi _{\alpha }$ like the scalar one-channel potentials. Only $V_{\alpha \alpha }$ are the minority among all others.  But nondiagonal elements seemed as some chaos of interactions. And suddenly it appears, that situation is rather simple. Almost as for scalar case if $\Psi_{\alpha}(x) has the same sign as $\Psi_{\beta}(x)$, but in contrast with independence of the rule of wave sign. Inverse situation is if there are opposite signs  of waves in corresponding channels at the given point $x$. Here is possible the unexpected {\bf inversion} of  influence their barriers and wells. Namely, for channel wave functions  $\Psi_{1}(x)$  and $\Psi_{2}(x)$  with opposite  signs  "{\bf barriers can be attractive(!)} and {\bf wells repulsive (!)}". Really $V_{12}(x)$  in the term $V_{12}(x) \Psi_{2}(x) $  in equation of the first channel in  the system  \ref{system2}  acts as potential with opposite sign when  $\Psi_{1}(x) $ and $\Psi_{2}(x) $ have different signs. To  explain  better let us write this   term in the form  $V_{12}(x) \frac{\Psi_{2}(x)}{\Psi_{1}(x)}  \Psi_{1}(x)  $  (multiplying and  dividing by the same function $\Psi_{1}(x)$)  as if with  {\bf  effective  single-channel (scalar) potential  $V_{12}(x) [\Psi_{2}(x)/ \Psi_{1}(x)] $, which has opposite sign relative to   $V_{12}(x)$  because of negative sign of  $[\Psi_{2}(x)/ \Psi_{1}(x)]$.  That is the barriers in   $V_{12}(x)$ contribute to bending  $\Psi_{1}(x) $ TO THE AXIS $x$, and it s wells act conversely to turn  $\Psi_{1}(x) $ FROM AXIS $x$ and so influence  in opposite manner in comparison with usual potentials  on the intensity  ($-\Psi”_{1}(x) $  of bending $\Psi_{1}(x) $  TO/FROM AXIS $x$. Meanwhile in the second channel happens the analogous inversion.  The corresponding unusual, but nevertheless simple rules are useful for understanding some previously mysterious quantum peculiarities. It is illustrated by different examples, e.g. complex  potentials [4], periodic structures, transparent interaction matrices etc.
For similar signs of channel functions  $\Psi _{\alpha }, \, \Psi_{\beta }$ the situation is standard one: the elements of interaction matrices $V_{\alpha \beta }$ are like the usual scalar potentials and diagonal matrix elements $V_{\alpha \alpha }$.  Their wells (and barriers) increase (and decrease)the bending intensity of partial waves to the $x$ axis.
Barriers in $V_{11}(x)$ and $V_{12}(x)$ in both terms $-V_{11}(x))\Psi_{1}(x)$ and $-V_{12}(x)\Psi_{2}(x)$ in the first equation are subtracted from the energy value $E_{1}$ and make smaller the bending intensity |$\Psi"_{1}(x)$|.
Analogously act the potential matrix elements in the second
equation in \ref{system2}. Wells in $V_{12}(x)$ change
|$\Psi"_{1}(x)$| and |$\Psi"_{2}(x)$| also as in diagonal matrix
elements $V_{11}(x)$ and $V_{22}(x)$.


Model of the “impossible” bound state under the potential barrier. Although this is a trivial? Multichannel model of coupled  equations, which could be
Separated (transformed into Schroedinger equation without coupling, the prediction of such exotic state  was made before we understood this , without any help of consideration of simplifying possibility of уничтожения зацепления уравнений.

The consideration of wave bending helps the deeper understanding of periodicity?  This is an  significant step to solve qualitatively systems of coupled equations  'in mind'. So could be explained the mechanism of simultaneous permanent
resonance in channels with different thresholds which  seemingly
violate the necessary equality of "average channel kinetic
energies" on the periods.  But it can be compensated by terms
with  effective  potentials representing the influence of $V_{12}$ (details will be presented elsewhere.), see also [1] 2000.  We must only mention that the system of two ordinary differential equations can have two branches of band spectra with overlaps of forbidden zones.

ПОВТОРЫ?
For understanding the resonance mechanism of spectral gap creation for waves motion in periodical potentials we used the notion of energy level shifts in
infinite rectangular well when shifted states at different energy values have the same wave length. Now we get explanation how the length of different channel waves corresponding to different thresholds are commensurable due to the action of  of interaction matrix. Although the zero boundary conditions at the common vertical potential walls of different channels will automatically provide commensurable wave length of space oscillations, but it remained unclear, what special role play here separate elements of interaction matrix. The significance of the notion about the ‘normal’ and ‘inverse’ influence of $V_{12}(x)$ becomes more apparent if we consider improbable situation that nobody knows now trivial fact that the potential barrier is repulsive and well attractive.
 
\begin{thebibliography}{99
}    
???? [1] Б.Н. Захарьев, В.М. Чабанов «Послушная квантовая механика. Новый статус теории в подходе обратной задачи», Институт Компьютерных Исследований, М. 2002. Русскую версию книги можно свободно скачать в Интернете на сайте
http://theor.jinr.ru/~zakharev/.\\
Только что опубликована  усовершенствованная английская  версия книги : Zakhariev B.N., Chabanov V.M., “Submissive Quantum Mechanics.  New Status of the Theory  in Inverse Problem Approach”, Nova Science Publishers, New York, 2007. Вводная ее часть (а особо заинтересованным и вся книга) могут быть высланы бесплатно по электронной почте zakharev@theor.jinr.ru ;\\
Inverse Problems, (topical review), {\bf 13}, R47-R79 (1997);\\

[??]    Zakhariev B.N. CONCEPTION OF GENERAL ABILITY TO MAKE DISCOVERIES. Joys of Creative life to Everybody;   Concepts of P p. 335-347, 2006. Расширенную русскую версию этой статьи можно   свободно прочитать и скачать с нашего сайта, указанного в [1].
 
[2] Новое в поведении волн в прозрачных, периодических и многоканальных структурах, Физика ЭЧАЯ, 36, N6 (2005) 1505-1545 .\\
Ann.Phys. (N.Y.) {\bf 285} 1-24, 2000
hysics, Vol.III,

1-24, 2000; New situation in quantum
Mechanics  (wonderful potentials from the inverse problem).\\

[3] Chabanov V.M., Zakhariev B.N., To the Theory of Waves in
Periodic Structures in Inverse Problem Approach, Int. J. Mod.
Phys. 18, N 30 (2004)  3941-3957; \\

V.M.Chabanov, B.N.Zakhariev, et al, in “Lecture Notes in Physics”, Inverse and Algebraic  Quantum Scattering, 1997, Springer, p. 197, 1993.

[7] И.В. Амирханов, Б.Н. Захарьев, ЖЭТФ, 1965, т.49, 1097.
  Жигунов В.П., Захарьев Б.Н. «Методы сильной связи каналов в квантовой теории рассеяния

\end{thebibliography}

\end{document}



РУССКИЙ ТЕКСТ

Парадокс научного взаимодействия с Я.А. состоял в том, что за десять лет у нас не появилось ни одной совместной публикации.

-


и положительную сторону. Редкая свобода, хотя и возникла из-за «экономии» времени руководителем, но в то же время способствовала  самостоятельности его учеников. Положительный эффект оказался более сильным. Такой свободы творчества не было (редко) кому удалось испытать в нашем институте.
История открытия метода усеченных асимптотик (Эфрос, Смородинский). Именно Смородинский объяснил мне трудность использования гипер-сферических базисных функций в задачах рассеяния, оказавшихся такими эффективными при описании локализованных  (объяснить бы это чудо

Это был полезный опыт разбиения (разрезания) волновой функции для упрощения расчетов. Например, вы(от)деление асимптотик, имеющих особенно простой вид произведения функций, имеющих вид невзаимодействующих ядерных подсистем.
Этот прием оказался решающим для преодолении трудностей описания ядерных реакций с перераспределением частиц. Обобщение формализма единой теории ядерных реакций с переменным составом промежуточных кластеров.

 Я.А.,  несмотря на недостаток взаимопонимания, не хотелось тратить на нас время (ни на беседы, ни на поиск задач, которые были бы нам по силам),  многие намеки на возможные перспективные направления  были нами использованы в дальнейшем , иногда после долгого перерыва (например, квантовая обратная задача для Б.З.).

 Гельфанда-Левитана и Марченко Смородинский обратил наше внимание на это замечательное событие, предложив проделать некоторые расчеты по нахождению ядерных сил. В результате мы даже послали с В.Б. Беляевым статейку в журнал, которую Я.А. вскоре изъял из редакции из опасения критики со стороны математиков. У Я.А. тогда состоялась какая-то беседа с классиком обратной задачи Борисом Моисеевичем Левитаном, который раскритиковал (поругал) Я.А. , так что напуганный этим наш научный руководитель счел благоразумным замести следы нашей попытки «внести свой вклад в развитие нового направление ядерной физики». Наверное, это было правильно, так как мы тогда  смутно представляли себе суть формализма обратной задачи.


-Реванш  у Левитана: сначала, кажется, понравился (Б.М. зауважал) за оригинальные социальные идеи, где я чувствовал себя как рыба в воде. А позднее мой доклад об уроках квантовой интуиции на основе ОЗ  на открытии конференции по ОЗ  (озеро Балатон, в Венгрии) оказался для него сюрпризом (он и не представлял себе, что его собственный формализм + СУЗИ Кв. Мех способен был скрывать даже от его отцов-основателей столько чудес (вы мне нравитесь).

Долгий период традиционного использования  некорректно поставленной обратной задачи и поиска способов регуляризации решения.
Период  (обобщения? ) попыток сформулировать подходы к многомерным обратным задачам Л.Д.Фаддеев; Хенкин и Новиков, Ньютон. Визит Ньютона и попытка организовать перевод книги Ньютона. Смородинский обещал посодействовать, но  здесь, наверное, помешало то, что Я.А. не мог смириться с тем, что ОЗ не поддалась ему сразу и у него выработался (комплекс неполноценности вместе с крепкой неприязнью к ОЗ. Так что перевод не был одобрен издательством МИР, куда в редсовет входил Я.А.

Обман Калинкина помочь защите Докт, канд? (Я Ваш верный союзник, как оппонент, хотя имеются много паротивников???) Диссертации (если извиняющие его обстоятельства?

Наконец, по совету Марченко, мы обратили внимание на точно решаемые модели ОЗ. Увлечение квантовыми картинками (тысячи)- подарок математиков, который они недостаточно рекламировали для физиков. Беспрецедентное совпадение качественной простоты (мгновенное предсказание результатов приближенно качественных: число пиков и ям возмущающего взаимодействия для элементарных спектральных преобразований  и абсолютной точности численных расчетов.
Замечательно, что эти качественные правила оказались применимыми и к прямым задачам, хотя без дополнительной возможности точных расчетов.
Прорыв в определении простейших правил элементарных спектральных преобразований.
Фундаментальные составляющие волн и потенциалов.

С каким бы удовольствием мы бы сейчас рассказали теорию ? (а разве сам Смородинский не похвалил китайцу книгу «Уроки кантовой интуиции»? или сейчас можно было бы это сделать еще проще и убедительнее (сомневаюсь).

Рис ………………..

Более сложный пример без расцепления.

Объяснения Ч-блок прозрачности? В терминах изгибов волновых функций.

Некоторая поверхностность подхода Я.А. которую многие оценивают как его недостаток, по-моему имел частичным продолжением наши успехи в решении квнтовых задач качественно в уме, что мне представляется высшим достирежением в понимании физической сути (сущности) Жигунов В.П., Захарьев Б.Н. «Методы сильной связи каналов в квантовой теории рассеяния.               

ЛИТЕРАТУРА

\begin{thebibliography}{99
}    
???? [1] Б.Н. Захарьев, В.М. Чабанов «Послушная квантовая механика. Новый статус теории в подходе обратной задачи», Институт Компьютерных Исследований, М. 2002. Русскую версию книги можно свободно скачать в Интернете на сайте
http://theor.jinr.ru/~zakharev/.\\
Только что опубликована  усовершенствованная английская  версия книги : Zakhariev B.N., Chabanov V.M., “Submissive Quantum Mechanics.  New Status of the Theory  in Inverse Problem Approach”, Nova Science Publishers, New York, 2007. Вводная ее часть (а особо заинтересованным и вся книга) могут быть высланы бесплатно по электронной почте zakharev@theor.jinr.ru ;\\
Inverse Problems, (topical review), {\bf 13}, R47-R79 (1997);\\

[??]    Zakhariev B.N. CONCEPTION OF GENERAL ABILITY TO MAKE DISCOVERIES. Joys of Creative life to Everybody;   Concepts of P p. 335-347, 2006. Расширенную русскую версию этой статьи можно   свободно прочитать и скачать с нашего сайта, указанного в [1].
 
[2] Новое в поведении волн в прозрачных, периодических и многоканальных структурах, Физика ЭЧАЯ, 36, N6 (2005) 1505-1545 .\\
Ann.Phys. (N.Y.) {\bf 285} 1-24, 2000
hysics, Vol.III,

1-24, 2000; New situation in quantum
Mechanics  (wonderful potentials from the inverse problem).\\

[3] Chabanov V.M., Zakhariev B.N., To the Theory of Waves in
Periodic Structures in Inverse Problem Approach, Int. J. Mod.
Phys. 18, N 30 (2004)  3941-3957; \\

V.M.Chabanov, B.N.Zakhariev, et al, in “Lecture Notes in Physics”, Inverse and Algebraic  Quantum Scattering, 1997, Springer, p. 197, 1993.


[7] И.В. Амирханов, Б.Н. Захарьев, ЖЭТФ, 1965, т.49, 1097.


  Жигунов В.П., Захарьев Б.Н. «Методы сильной связи каналов в квантовой теории рассеяния