On Eisenbud’s and Wigner’s R-matrix: A general approach
نویسندگان
چکیده
The main objective of this paper is to give a rigorous treatment of Wigner’s and Eisenbud’s R-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite deficiency indices. In the framework of boundary triplets and associated Weyl functions an abstract generalization of the R-matrix method is developed and the results are applied to Schrödinger operators on the real axis. 2000 Mathematical Subject Classification: 47A40, 34L25, 81U20
منابع مشابه
Global conjugate gradient method for solving large general Sylvester matrix equation
In this paper, an iterative method is proposed for solving large general Sylvester matrix equation $AXB+CXD = E$, where $A in R^{ntimes n}$ , $C in R^{ntimes n}$ , $B in R^{stimes s}$ and $D in R^{stimes s}$ are given matrices and $X in R^{stimes s}$ is the unknown matrix. We present a global conjugate gradient (GL-CG) algo- rithm for solving linear system of equations with multiple right-han...
متن کاملAn Algebraic Approach to Wigner’s Unitary-antiunitary Theorem
We present an operator algebraic approach to Wigner’s unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert modules over matrix algebras. We also present a Wignertype result for maps on prime C-algebras. 1991 Mathematics subject classification (Amer. Math. Soc.): primary...
متن کاملA characterization of multiwavelet packets on general lattices
The objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $Gamma$ in $mathbb R^d$ by virtue of time-frequency analysis, matrix theory and operator theory.
متن کاملSymmetry projection of the rovibrational functions of methane
In this work we propose a symmetry projection approach to build a rovibrational basis for methane. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigner’s D functions and vibrational matrix representations provided by a local scheme. The proposed approach is gene...
متن کاملWigner’s D-matrix elements for SU(3) - A Generating Function Approach
A generating function for the Wigner’sD-matrix elements of SU(3) is derived. From this an explicit expression for the individual matrix elements is obtained in a closed form. PACS number(s): Typeset using REVTEX ∗[email protected] 1
متن کامل