Computer Study of the Proton-Electron-Positron System by a Variational Method

  • P. U. Arifov
  • V. M. Mal’yan


The variational method [1] of studying many-particle systems lies in minimizing the energy functional
$$E = \frac{{\int {\psi *\mathop H\limits^\Lambda \psi d\tau } }} {{\int {\left| \psi \right|^2 d\tau } }} = \min $$
by means of an appropriately-constructed test (trial) function (based on physical and other considerations), constituting a certain approximation to the true eigenfunction of the ground state of the system; the resultant minimum energy Emin gives the upper limit to the eigenvalue of the energy of this state.


Helium Atom Trial Function Computer Study Positron Retardation Angular Correlation Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Bethe and E. Solpiter, Quantum Mechanics of Atoms with One and Two Electrons [Russian translation], Fizmatgiz, Moscow (1960).Google Scholar
  2. 2.
    P. U. Arifov, Dokl, Akad, Nauk Uzbek. SSR, 3:18 (1967).Google Scholar
  3. 3.
    T. Chandrasekhar, Astrophys. J., 100:176 (1944).ADSCrossRefGoogle Scholar
  4. 4.
    V. P. Shmelev, Zh. Eksp. Teor. Fiz., 37:458 (1959); 38:1528 (1960); Author’s abstract of Candidate’s Dissertation, Moscow State University (1960).Google Scholar
  5. 5.
    Din-Van-Khoang, zn, Eksp. Teor. Fiz., 49:630 (1965); Author’s abstract of Candidate’s Dissertation, Belorussian State University (1965).Google Scholar
  6. 6.
    P. U. Arifov, V. I. Gol’danskii, and Yu. S. Sayasov, Izv. Akad. Nauk Uzbek SSR, Ser. Fiz.-Mat. Nauk, No.5, p. 48 (1966).Google Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • P. U. Arifov
  • V. M. Mal’yan

There are no affiliations available

Personalised recommendations