Harmony in many-particle quantum problem

K.V. Chukbar^a, b
^aNational Research Centre ‘Kurchatov Institute’, pl. akad. Kurchatova 1, Moscow, 123182, Russian Federation
^bMoscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation

The model quantum problem of a harmonically trapped cloud of identical nonrelativistic particles interacting via harmonic oscillator potential has an exact solution which can be used to assess the efficiency of approximate methods standardly used in more realistic many-particle calculations.

Keywords: many-particle Shrödinger equation, harmonic oscillator, fermions, bosons, Thomas—Fermi equation
PACS: 03.65.−w, 05.30.Fk, 05.30.Jp, 31.15.bt (all)
DOI: 10.3367/UFNe.2017.06.038159
URL: https://ufn.ru/en/articles/2018/4/d/
Web of Science

000439002500004
Scopus

2-s2.0-85050598688
ADS NASA

2018PhyU...61..389C
Citation: Chukbar K V "Harmony in many-particle quantum problem" Phys. Usp. 61 389–396 (2018)

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Received: 3rd, April 2017, revised: 5th, June 2017, accepted: 21st, June 2017

Оригинал: Чукбар К В «Гармония в многочастичной квантовой задаче» УФН 188 446–454 (2018); DOI: 10.3367/UFNr.2017.06.038159

References (16) ↓ Cited by (1) Similar articles (20)

Landau L D, Lifshits E M Kvantovaya Mekhanika. Nerelyativistskaya Teoriya (M.: Nauka, 1974); Per. na angl. yaz., Landau L D, Lifshitz E M Quantum Mechanics. Non-Relativistic Theory (Oxford: Pergamon Press, 1965)
Bureeva L A, Lisitsa V S Vozmushchennyi Atom (M.: IzdAT, 1997)
Migdal A B, Krainov V P Priblizhennye Metody Kvantovoi Mekhaniki (M.: Nauka, 1966); Per. na angl. yaz., Migdal A B, Krainov V Approximation Methods In Quantum Mechanics (New York: W.A. Benjamin, 1969)
Kadomtsev B B, Kadomtsev M B Usp. Fiz. Nauk 167 649 (1997); Kadomtsev B B, Kadomtsev M B Phys. Usp. 40 623 (1997)
Pitaevskii L P Usp. Fiz. Nauk 168 641 (1998); Pitaevskii L P Phys. Usp. 41 569 (1998)
Arnol’d V I Matematicheskie Metody Klassicheskoi Mekhaniki (M.: Nauka, 1974); Per. na angl. yaz., Arnold V I Mathematical Methods Of Classical Mechanics (New York: Springer-Verlag, 1978)
Landau L D, Lifshits E M Mekhanika (M.: Nauka, 1973); Per. na angl. yaz., Landau L D, Lifshitz E M Mechanics (Oxford: Pergamon Press, 1976)
Dodonov V V, Man’ko V I "Kvantovanie, gravitatsiya i gruppovye metody v fizike" Trudy FIAN 152 145 (1983)
Akhundova E A, Dodonov V V, Man’ko V I Teor. Mat. Fiz. 60 413 (1984); Akhundova É A, Dodonov V V, Man’ko V I Theor. Math. Phys. 60 907 (1984)
Kaplan I G Simmetriya Mnogoelektronnykh Sistem (M.: Nauka, 1969); Per. na angl. yaz., Kaplan I G Symmetry Of Many-Electron Systems (New York: Academic Press, 1975)
Haas F et al. Phys. Plasmas 10 3858 (2003)
Hossen M A, Mamun A A Phys. Plasmas 22 073505 (2015)
Philippidis C, Bohm D, Kaye R D Nuovo Cimento B 71 75 (1982)
Bohm D Phys. Rev. 85 166 (1952)
Rumer Yu B, Ryvkin M Sh Termodinamika, Statisticheskaya Fizika i Kinetika (M.: Nauka, 1977); Per. na angl. yaz., Rumer Yu B, Ryvkin M Sh Thermodynamics, Statistical Physics, And Kinetics (Moscow: Mir, 1980)
Prudnikov A P, Brychkov Yu A, Marichev O I Integraly i Ryady Vol. 2 (M.: Fizmatlit, 2003); Per. na angl. yaz. pred. izd., Prudnikov A P, Brychkov Yu A, Marichev O I Integrals And Series Vol. 2 (New York: Gordon and Breach, 2002)