On the algebraic properties of the Luttinger model

  • K. A. Rustamov
Session IX — Statistical Mechanics
Part of the Lecture Notes in Physics book series (LNP, volume 180)


The systems of differential equations for the elements of the tangent vector field corresponding to the Lie group of equivalence of the Schrödinger equations family with the Luttinger type Hamiltonian depending on an arbitrary potential function are analyzed. The absense of any operator of the first order in linear momentum operator in the Lie algebra of invariance of the problem has been proved. The obtained equations in the limitσ = 0 of the parameters enable one to get the Lie groups of equivalence of a various problems of quantum mechanics. In the case of σ = 0 the kernel of the basic groups of the mentioned family of equations is demonstrated to be physically trivial.


Equation Family Basic Algebra Field Corres Tangent Vector Field Nonrelativistic Quantum Mechanic 
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/.
    J.M.Luttinger, Phys.Rev.,102, 1030 1956.Google Scholar
  2. /2/.
    I.A.Malkin,V.I.Man'ko, Dinamicheskie simmetrii i cogerentnye sostoiania quantortrykh sistem,Nauka 1979Google Scholar
  3. /3/.
    L.V.Ovsiannikov,Gruppovoi analiz differencialnykh uravnenii, Nauka, 1978.Google Scholar
  4. /4/.
    V.I.Fuschich,Teoretiko-gruppovie metody v matematichemkoi fisike, Kiev 1978Google Scholar
  5. /5/.
    M.A.Shubin,Psevdodiflerencialnye operatory i spectralnaia teoria, Nauka, 1978.Google Scholar
  6. /6/.
    W.Miller,Jr.,Symmetry and Separation of Variables, 1977.Google Scholar
  7. /7/.
    U.Niederer,Helvetica Phys.Acta,45,802,1972;47,119, 1974.Google Scholar
  8. /8/.
    R.L.Anderson,Revista Mexicana de Fisica,21,1,1972; J.Math.Phys. 14, N 11, 1973.Google Scholar
  9. /9/.
    F.M.Gashimzade,K.A.Rustamov,Doklady Akademii Nauk Azerbaijanskoi SSR, N 321, 1978.Google Scholar
  10. /10/.
    M.A.Mekhtiev (to be published).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • K. A. Rustamov
    • 1
  1. 1.Institute of PhysicsAcademy of Sciences of the Azerbaijan SSRBakuUSSR

Personalised recommendations