Showing papers on "Schwinger variational principle published in 1981"

Extension of the Schwinger variational principle beyond the static-exchange approximation

Abstract: We propose a new vairational principle for scattering theory which extends the Schwinger variational principle beyond the static-exchange approximation and to inelastic scattering. Application of this formulation to the scattering of electrons by hydrogen atoms at energies below k^2=0.64 demonstrates the rapid convergence of the phase shift with respect to the number of basis functions for both the open- and closed-channel orbitals. Furthermore, we show that the convergence of the phase shift with respect to the number of expansion functions (exact states or pseudostates) is also fast. In our theory, the resulting phase shifts can be more accurate than those of the close-coupling method even if the same expansion basis is used. The phase shifts in our 1s-2s―-2p― calculation are comparable to those of 1s-2s-2p-3p―-3d― calculation of Matese and Oberoi [Phys. Rev. A 4, 569 (1971)], which are very close to the exact values. Several aspects of the convergence characteristics are also discussed.

Iterative approach to the Schwinger variational principle applied to electron—molecular-ion collisions

Abstract: We present a study of electron—molecular-ion collisions. The scattering equations are solved using an iterative approach to the Schwinger variational principle. These equations are formulated using the Coulomb Green's function to properly treat the long-range Coulomb tail of the molecular-ion potential. We apply this approach to electron—hydrogen-molecular-ion collisions in the static-exchange approximation. We obtain elastic differential cross sections, and also use the continuum states from these calculations to compute the photoionization cross section of the hydrogen molecule. The iterative method used here converged rapidly in all calculations performed.

Variational scattering theory using a functional of fractional form. I. General theory

Abstract: We propose a variational method for scattering in which the functional is of a fractional form as for the Schwinger variational principle. However, our functional does not involve the Green's function, but the Hamiltonian and the potential function. This method shows features of both the Schwinger-type variational principles and the Kohn-type standard variational principles. As a result, our method can derive distinct advantages from both of these approaches. The resultant K matrix is symmetric and anomaly-free. Some other properties, including a minimum principle, which is useful in the selection of an optimum basis for the expansion of the scattering functions are also discussed.

Schwinger variational calculations for electron scattering by polar molecules

Abstract: The authors present the results of applications of the Schwinger variational principle to the scattering of low-energy electrons by the strongly polar molecule LiH. The method is based on an iterative approach which uses the Schwinger variational principle to solve the Lippmann-Schwinger integral equation for the scattering wavefunction. The procedure uses trial scattering wavefunctions which contain both discrete basis functions and numerical continuum wavefunctions which satisfy explicitly the scattering boundary conditions. The results of these applications show that the method is an effective approach to the solution of the electron-molecule scattering equations. Several details of the method are discussed.

Application of a new variational functional for electron-molecule collisions: an extension of the Schwinger variational principle

Abstract: Discusses a variational functional for scattering theory which has been recently proposed by Takatsuka and McKoy (1980). It is shown that this functional can provide results with a purely discrete set of functions which are approximately equivalent to those obtained by Lucchese et al. (1980) from the first iteration of the iterative Schwinger method. Applications to the scattering of electrons by systems including CO+ and LiH illustrate this relationship and other features of the method.

Variational principle for derivation of macroscopic equations

Abstract: It is pointed out that the Schwinger variational principle of scattering theory applies to the case of linear and nonlinear relaxation problems in quantum statistics. By means of this principle it is possible to derive closed sets of equations for expectation values. To illustrate this variational method and to clarify the connection to other standard approaches some simple examples are treated for which the equations of motion are already known.

Variational Principle for Derivation Equations

Abstract: It is pointed out that the Schwinger variational principle of scattering theory applies to the case of linear and nonlinear relaxation problems in quantum statistics. By means of this principle it is possible to derive closed sets of equations for expectation values. To illustrate this variational method and to clarify the connection to other standard approaches some simple examples are treated for which the equations of motion are already known.