相关论文: An efficient approach for spin-angular integration…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…
Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial…
This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage,…
In this paper a library for spin--angular integration in LS-coupling for many-electron atoms is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum…
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version…
The three-particle operator in a second quantized form is studied. The operator is transformed into irreducible tensor form. Possible coupling schemes, distinguished by the classes of symmetric group \mathrm{S_{6}}, are presented.…
A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric…
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the $n$-fold antisymmetrized tensor product $\wedge^n V_u$, where $n$ is the number of electrons and $u =…
A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the…
Using the irreducible tensor-operator technique, we establish the relation between different forms of spin tomograms. Quantizer and dequantizer operators are presented in simple explicit forms and are specified for the low-spin states. The…
The general tensorial form of the orbit-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements with respect to…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…
An alternative method to the density matrix formalism for the derivation of general expressions of the interaction of polarized atoms with polarized photons and electrons is presented. The expression for the cross-section describing the…