We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Reduced Matrix Elements for Symmetry-Constructed Systems.
- Authors
Ellzey Jr, Marion Lawrence
- Abstract
Eigenvalue problems involving symmetry, such as the Schrödinger equation when the Hamiltonian commutes with a group, can generally be reduced in size using group theoretical techniques such as the Wigner-Eckart theorem. The key step is calculation of the reduced matrix elements followed by eigenvalue determination by the secular equation. For finite groups it is usual to obtain reduced matrices by transformation to the symmetry adapted basis. Direct determination of reduced matrix elements by some means would be computationally more efficient with better precision. It is shown here that this direct determination is possible to some extent for symmetry-constructed systems such as symmetry-generated molecules. A simple illustration is given using the Hûckel treatment of the cyclopropenyl radical.
- Subjects
SYMMETRY (Physics); EIGENVALUES; HAMILTONIAN systems; MATRICES (Mathematics); MATHEMATICS theorems; MATHEMATICAL analysis; PHYSICAL &; theoretical chemistry research
- Publication
Croatica Chemica Acta, 2013, Vol 86, Issue 4, p541
- ISSN
0011-1643
- Publication type
Article
- DOI
10.5562/cca2307