Yurii Shirokov

Yurii Shirokov, (Широков, Юрий Михайлович 21.6.1921—5.7.1980), writer, physicist, professor.Graduated from Moscow State University (Moscow) in 1948. Worked in the same university, then in the Steklov Mathematical Institute (Moscow). He wrote more than 100 scientific papersШироков Юрий Михайлович at "Biography" (in Russian),http://www.biografija.ru/show_bio.aspx?id=137184] and several monographs, among which the textbook "Nuclear Physics" is particularly relevant.cite book
author=Yu.M.Shirokov
coauthors=N.P.Yudin
title= Nuclear Physics
ISBN=13: 978-0828524513
year=1983
url=http://www.amazon.co.uk/Nuclear-Physics-Yu-M-Shirokov/dp/0828524513
publisher: (Imported Pubn)] .

Algebra of generalized functions

Yu.Shirokov had constructed the Algebra of Generalized functions cite journal
author=Yu.M.Shirokov
title = Algebra of one-dimensional generalized functions
journal=TMF
year=1979
volume=39
issue=3
pages=471–477
url=http://springerlink.metapress.com/content/w3010821x8267824/?p=5bb23f98d846495c808e0a2e642b983a&pi=3] cite journal
author=Yu.M.Shirokov
title=Algebra of three-dimensional generalized functions
journal=TMF
publisher=Springer New York
issn=0040-5779 (Print) 1573-9333 (Online)
volume=40
issue=3
year=1979
doi=10.1007/BF01032064
pages=790–794
url=http://springerlink.metapress.com/content/hg5w86077wnp2637/?p=5bb23f98d846495c808e0a2e642b983a&pi=0] . Then it was applied to various systemscite journal
author=O.G.Goryaga
coauthors=Yu. M. Shirokov
title=Energy levels of an oscillator with singular concentrated potential
journal=TMF
year=1981
volume=46
number=3
pages=321–324
url=http://www.springerlink.com/content/k2164755540243kw/] cite journal
author=S.V.Talalov
coauthors=Yu.M.Shirokov
title=Interaction of a charged particle with an external electromagnetic field in the presence of a strongly singular potential
journal=TMF
publisher=Springer New York
issn=0040-5779 (Print) 1573-9333 (Online)
volume=46
issue=3
year=1981
doi=10.1007/BF01032728
url=http://springerlink.metapress.com/content/n620p80368770623/?p=2dec3e2814434eef9b18c6eeace9841d&pi=36
pages=207–210] cite journal
author=G. K. Tolokonnikov
title=Differential rings used in Shirokov algebras
journal=TMF
volume=53
issue= 1
year=1982
url=http://springerlink.metapress.com/content/nlnq818641568706/?p=ec1cea4940d049e9a606f4895c63e296&pi=6
doi=10.1007/BF01014789
pages=952–954] .

Classical and quantum mechanics

Shirokov was, perhaps, not the first to mention that quantum mechanics has many classical limits. The Planck constant $~hbar~$ appears in many relations, and there are many options to keep some of parameters (or even to vary them all) as $~hbar\; ightarrow\; 0~$. The most known limiting cases of quantum mechanics are classical waves and Newtonian mechanics. Shirokov has systematised the construction of classical limits of quantum mechanics, seecite journal
author=Yu.M.Shirokov
title=Perturbation theory with respect to Planck's constant
journal=TMF
publisher =Springer New York
issn=0040-5779 (Print) 1573-9333 (Online)
volume=31
issue=3
year=1977
doi=10.1007/BF01030565
pages=488–492
url=http://springerlink.metapress.com/content/l7h814r038750752/?p=5567f939c2764f8eaba7e8e684101a40&pi=24] .

Development of Shirokov's ideas

The most important ideas about the quantum mechanics and the theoretical physics in general formulated by Shirokov are not yet developed cite journal
doi=10.1070/PU1981v024n06ABEH004852
author=N N Bogolyubov
coauthors= S N Vernov, V S Vladimirov, A A Logunov, M K Polivanov, V E Troitskiĭ, D V Shirokov
title= Yuriĭ Mikhaĭlovich Shirokov (Obituary)
journal=Sov.Phys.Uspekhi
year=1981
volume=24
issue=6
pages= 526–527
url=http://www.turpion.org/php/paper.phtml?journal_id=pu&paper_id=4852] . In particular, the field theory in terms of wave packets (i.e., without divergent terms and without divergent series) is not yet constructed.

References