Representation of a complex Green function on a real basis: Integral representation
نویسندگان
چکیده
منابع مشابه
Representation of a complex Green function on a real basis
When the Hamiltonian H of a system is represented by a finite matrix H, constructed from a discrete basis with overlap matrix B, the matrix representation G(E) ≡ 1/(EB−H) of the resolvent G(E) = 1/(E − H) covers only one branch of G(E). We show how all branches can be specified by the phase φ of a complex unit of time tφ ≡ t0e. This permits H to be constructed on a real basis; the only duty of ...
متن کاملRepresentation of a complex Green function on a real basis: I. General Theory
When the Hamiltonian H of a system is represented by a finite matrix H, constructed from a discrete basis with overlap matrix B, the matrix representation G(E) ≡ 1/(EB−H) of the resolvent G(E) = 1/(E − H) covers only one branch of G(E). We show how all branches can be specified by the phase φ of a complex unit of time tφ ≡ t0e. This permits H to be constructed on a real basis; the only duty of ...
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6. M. Riesz, Sur la sommation des séries de Dirichlet, C. R. Acad. Sci. Paris vol. 149 (1909) pp. 18-21. 7. -, Sur Véquivalence de certaines méthodes de sommation, Proc. London Math. Soc. (2) vol. 22 (1923-1924) pp. 412-419. 8. L. L. Silverman, On the definition of the sum of a divergent series. University of Missouri Studies, Mathematical Series, vol. 1, no. 1, 1913. 9. O. Toeplitz, Über allge...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2000
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.62.062705