Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries

被引：15

作者：

Lemus, Renato ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Nucl Phys, Mexico City 04510, DF, Mexico

来源：

SYMMETRY-BASEL | 2012年 / 4卷 / 04期

关键词：

quantum numbers; discrete systems; symmetry projection; eigenfunction method; H-3(+); CH4;

D O I：

10.3390/sym4040667

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps) associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalues of the class operators (character table). The need of a canonical chain of groups to establish a complete set of commuting operators is emphasized. This analysis allows us to establish in natural form the connection between the quantum numbers and the eigenfunction method proposed by J.Q. Chen to obtain symmetry adapted functions. We then proceed to present a friendly version of the eigenfunction method to project functions.

引用

页码：667 / 685

页数：19

共 23 条

[11] Frank A., 2005, Symmetry Methods in Molecules and Nuclei
[12] Angular pseudomomentum theory for the generalized nonlinear Schrodinger equation in discrete rotational symmetry media
Garcia-March, M. -A.
Ferrando, A.
Zacares, M.
Vijande, J.
Carr, L. D.
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2009, 238 (15) : 1432 - 1438
[13] GIBSON WM, 1976, CAMBRIDGE MONOGRAPHS
[14] Greiner W., 1976, QUANTUM MECHANICS SY
[15] Hamermesh M., 1989, Group Theory and Its Application to Physical Problems
[16] Harter W. G., 1993, Principles of Symmetry, Dynamics, and Spectroscopy
[17] Kim S.K., 1999, GROUP THEORETICAL ME, P149
[18] A general method to obtain vibrational symmetry adapted bases in a local scheme
Lemus, R
[J]. MOLECULAR PHYSICS, 2003, 101 (16) : 2511 - 2528
[19] Stancu F., 1959, GROUP THEORY SUBNUCL
[20] Tsukerblat B.S., 1963, CHEM APPL GROUP THEO

← 1 2 3 →