Green’s Functions and Perturbation Theory

Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 7)


In this chapter we are interested in finding the eigenvalues and eigenfunctions of a hamiltonian H which can be decomposed as
$$ H = {H_0} + {H_1}; $$
H 0 is such that its eigenvalues and eigenfunctions can be easily determined. This problem will be solved by: 1) calculating G 0(z) corresponding to H 0 ; 2) expressing G(z) in terms of G 0(z) and H 1, where G(z) is the Green’s function associated with H; and 3) extracting from G(z) information about the eigenvalues and eigenfunctions of H.


Total Cross Section Continuous Spectrum Differential Cross Section Discrete Level Discrete Eigenvalue 
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  1. 4.1
    A.L. Fetter, J.D. Walecka: Quantum Theory of Many-Particle Systems (McGraw-Hill, New York 1971)Google Scholar
  2. 4.2
    L.I. Schiff: Quantum Mechanics, 2nd ed. (McGraw-Hill, New York 1955)zbMATHGoogle Scholar
  3. 4.3
    L.D. Landau, E.M. Lifshitz: Quantum Mechanics (Addison-Wesley, Reading, Mass. 1958)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of VirginiaCharlottesvilleUSA

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