Abstract
We present a scheme for a rapid solution of a general three-dimensional Schrödinger equation. The Hamiltonian operator is discretized on a point grid using the finite-difference method. The eigenstates, i.e., the values of the wave functions in the grid points, are searched for as a constrained (due to the orthogonality requirement) optimization problem for the eigenenergies. This search is performed by the conjugate-gradient method. We demonstrate the scheme by solving for the self-consistent electronic structure of the diatomic molecule P2 starting from a given effective electron potential. Moreover, we show the efficiency of the scheme by calculating positron states in low-symmetry solids.
Original language | English |
---|---|
Pages (from-to) | 14057-14601 |
Number of pages | 5 |
Journal | Physical Review B |
Volume | 51 |
Issue number | 20 |
DOIs | |
Publication status | Published - 15 May 1995 |
MoE publication type | A1 Journal article-refereed |
Keywords
- conjugate-gradient
- electronic-structure calculations
- finite-difference