Abstract
A purely algebraic approach to Green’s functions is presented. It allows the computation of Green’s functions by means of an eigenvalue problem as small as possible for a given accuracy. This is achieved by formulating a unitary transformation of the Hamiltonian matrix. The method is applied as an example to the particle-particle propagator. The case of a one-particle Hamiltonian is treated exactly for illustrative purposes and a unitary transformation is derived. A connection to effective Hamiltonian theory can be drawn. The general problem of a two-particle Hamiltonian is discussed as well and it is found that a quite straightforward generalization of the theory of one-particle Hamiltonians gives rise to systematic approximation schemes. The third order approximation scheme is derived and compared with the Algebraic Diagrammatic Construction approximation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A L Fetter and J D Walecka: “Quantum Theory of Many-Particle Systems”, McGraw-Hill, New York, 1971.
D J Thouless: “The Quantum Mechanics of Many-Body Systems”, Academic Press, New York, London, 1972.
N H March, W H Young, S Sampanthar: “The Many-Body Problem in Quantum Mechanics”, Cambridge University, Cambridge, 1967.
A A Abrikosov, L P Gorkov, I E Dzyaloshinski: “Methods of Quantum Field Theory in Statistical Physics”, Prentice Hall, New York, 1963.
E K U Gross and E Runge: “Vielteichentheorie”, B S Teubner, Stuttgart, 1986.
a)_A Tarantelli and L S Cederbaum, Phys Rev A, to be published b) A Tarantelli and L S Cederbaum, to be published.
A Tarantelli, PhD Thesis, Heidelberg, in preparation.
J Schirmer, Phys Rev, A26, 2395,(1982).
J Schirmer, L S Cederbaum, O Walter, Phys Rev A28, 1237, (1983).
J Schirmer and A Barth, Z Phys A317, 267, (1984).
B H Brandow, in “Effective Interactions and Operators in Nuclei”, Lecture Notes in Physics, Springer, Berlin, 1975; B H Brandow, Int J Quant Chem 15, 207, (1979).
V Kvasnicka, in Adv Chem Phys 36, Wiley, New York, 1977.
I Lindgreen and J Morrison, “Atomic many-Body theory”, Springer, Berlin, 1982.
a)_L S Cederbaum, H Köppel, W Domcke, Int J Quant Chem Symp 15, 251, (1981).
L S Cederbaum, J Schirmer, H-D Meyer, J Phys A, to be published.
F Tarantelli, A Tarantelli, A Sgamellotti, J Schirmer, L S Cederbaum, Chem Phys Lett 117, 577(1985);.
F Tarantelli, J Schirmer, A Sgamellotti, L S Cederbaum, Chem Phys Lett, 122, 169, (1985).
F Tarantelli, A Tarantelli, A Sgamellotti, J Schirmer, L S Cederbaum, J Chem Phys 83, 4683, (1985).
F Tarantelli, A Sgamellotti, L S Cederbaum, J Schirmer, ibid 86, 2201, (1987).
ibid 86, 2168, (1987).
I Shavitt, in “Methods of Theoretical Chemistry”, 3, ed H F Schaefer III, Plenum Press, New York, 1977; B Roos and P E M Siegbahn, ibid; B Roos, in “Computational Techniques in Quantum Chemistry and Molecular Physics”, ed G F Diercksen et al, D Reidel Publishing Co, Dordrecht, Holland, 1975.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Tarantelli, A., Cederbaum, L.S. (1989). On the Connection between Effective Hamiltonians and Propagators. In: Kaldor, U. (eds) Many-Body Methods in Quantum Chemistry. Lecture Notes in Chemistry, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93424-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-93424-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51027-7
Online ISBN: 978-3-642-93424-7
eBook Packages: Springer Book Archive