Abstract
Starting from the general decomposition of the many-body Hamiltonian parametrized by an operator {Lambda}we derive the class of `{Lambda}-transformed` perturbation series. Aiming at practical applications we consider many-body perturbation theory of atoms and molecules in finite dimensional Hilbert spaces. Investigation of the analyticity properties of the eigenvalues and eigenstates of the Hamiltonian as functions of the coupling parameter defined by the particular decomposition of H allows for the construction of (minimal) {Lambda}operators mapping an originally divergent series to a convergent one. There exists an operator {Lambda}{sub opt} leading to the exact results in first order. Further improvements of the above mentioned minimal {Lambda}operators can be achieved by approximations of {Lambda}{sub opt} leading to fast convergent perturbation series. As the size of the remaining perturbation is given by the {Lambda}operator chosen this method provides an a priori estimate of the convergence properties. (orig.)
Citation Formats
Schmidt, C.
On the systematic construction of convergent perturbation series; Zur systematischen Konstruktion konvergenter Stoerungsreihen.
Germany: N. p.,
1993.
Web.
Schmidt, C.
On the systematic construction of convergent perturbation series; Zur systematischen Konstruktion konvergenter Stoerungsreihen.
Germany.
Schmidt, C.
1993.
"On the systematic construction of convergent perturbation series; Zur systematischen Konstruktion konvergenter Stoerungsreihen."
Germany.
@misc{etde_10131445,
title = {On the systematic construction of convergent perturbation series; Zur systematischen Konstruktion konvergenter Stoerungsreihen}
author = {Schmidt, C}
abstractNote = {Starting from the general decomposition of the many-body Hamiltonian parametrized by an operator {Lambda}we derive the class of `{Lambda}-transformed` perturbation series. Aiming at practical applications we consider many-body perturbation theory of atoms and molecules in finite dimensional Hilbert spaces. Investigation of the analyticity properties of the eigenvalues and eigenstates of the Hamiltonian as functions of the coupling parameter defined by the particular decomposition of H allows for the construction of (minimal) {Lambda}operators mapping an originally divergent series to a convergent one. There exists an operator {Lambda}{sub opt} leading to the exact results in first order. Further improvements of the above mentioned minimal {Lambda}operators can be achieved by approximations of {Lambda}{sub opt} leading to fast convergent perturbation series. As the size of the remaining perturbation is given by the {Lambda}operator chosen this method provides an a priori estimate of the convergence properties. (orig.)}
place = {Germany}
year = {1993}
month = {Dec}
}
title = {On the systematic construction of convergent perturbation series; Zur systematischen Konstruktion konvergenter Stoerungsreihen}
author = {Schmidt, C}
abstractNote = {Starting from the general decomposition of the many-body Hamiltonian parametrized by an operator {Lambda}we derive the class of `{Lambda}-transformed` perturbation series. Aiming at practical applications we consider many-body perturbation theory of atoms and molecules in finite dimensional Hilbert spaces. Investigation of the analyticity properties of the eigenvalues and eigenstates of the Hamiltonian as functions of the coupling parameter defined by the particular decomposition of H allows for the construction of (minimal) {Lambda}operators mapping an originally divergent series to a convergent one. There exists an operator {Lambda}{sub opt} leading to the exact results in first order. Further improvements of the above mentioned minimal {Lambda}operators can be achieved by approximations of {Lambda}{sub opt} leading to fast convergent perturbation series. As the size of the remaining perturbation is given by the {Lambda}operator chosen this method provides an a priori estimate of the convergence properties. (orig.)}
place = {Germany}
year = {1993}
month = {Dec}
}