An alternative way of solving secular equations for the Hamiltonian matrices of regular quasi-one-dimensional systems
✍ Scribed by V. Gineityte
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 997 KB
- Volume
- 60
- Category
- Article
- ISSN
- 0020-7608
No coin nor oath required. For personal study only.
✦ Synopsis
An alternative approach to secular problems for Hamiltonian matrices H of regular quasi-one-dimensional systems is suggested. The essence of this approach consists of the inverted order of operations against that of the traditional solid-state theory, viz., taking into account the local structure of the system is followed by regarding the translational symmetry of the whole chain. The first step is performed by reducing the initial system of secular equations into an effective N X N-dimensional secular problem, wherein a single equation corresponds to each of N elementary fragments of the initial chain. An implicit form of the dispersion relation and the level density function follow directly from the reduced problem without passing into the delocalized description of the system.
The resulting eigenfunctions of the matrix ff prove to be expressed as the Bloch sums of N nonorthogonal eigenvalue-dependent local-structure-determined orbitals of algebraic form, each of them corresponding to a definite elementary fragment of the chain. 0 1996 John Wiley & Sons, Inc. meric molecules and other extended quasi-onedimensional systems [ 1, 4-91. Cyclic boundary conditions are imposed on the chain under study in this case, and the first step toward solving the oncepts and methods of solid-state theory secular problem for the relevant one-electron C in the framework of the LCAO approxi-Hamiltonian matrix H consists of taking into acmation [l-41 are most commonly applied for the count the translational symmetry of the whole investigation of one-electron states of poly-chain. The usual way of doing this lies in passing