Publication: A transfer-matrix method for the determination of one-dimensional band structures
Loading...
Official URL
Full text at PDC
Publication Date
1993-01-07
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
IOP Publishing LTD
Citations
Exportar
Abstract
We show that the discretized forms of the Schrodinger and the Dirac equations for an arbitrary potential in one dimension are equivalent to the Poincare map of the corresponding wave equation for an array of delta-function potentials. Therefore, the dynamics of particles in general periodic potentials may be studied by means of an equivalent generalized Kronig-Penney model, in which there exist several delta-function potentials in each unit cell. Taking into account the techniques of dynamical systems, the transfer matrix method is then used in a simple form to compute the energy band edges and the dispersion law inside the allowed bands.
Description
© 1993 IOP Publishing Ltd
UCM subjects
Unesco subjects
Keywords
Citation
Albeverio S, Gesztesy F, Hoegh-Krohn R and Holden H 1988 Soluable Models in Quantum Mechanics (New Bellisard J, Formoso A, Lima Rand Testard D 1982 Phys. Rev. B 26 3024
Bernasconi J and Schneider T (ed) 1981 Physics in One Dimension (New York: Springer)
Dean P 1972 Rev. Mod. Phys. 44 127
Dominguez-Adame F 1989 J. Phys.: Condens. Matter 1 109
Dominguez-Adame F and GonzAlez M A 1992 Physic4 176B 180
Dominguez-Adame F and Macii E 1989 3. Phys. A: Math. Gen. 22 !A19
Dominguez-Adame F, MCndez B, Macii E and G o d l e z M A 1991 Mol. Phys. 74 1065
Dominguez-Adame F and Sinchez A 1991 Phys. Lett. 159A 153
Eldib A M, Hassan H F and Mohamed M A 1987 J. Phys. C: Solid State Phys. 20 3011
Kronig R Land Penney W B 1931 Proc. R Soc A 130 499
Lieb E H and Mattis D C 1966 Mathematical Physies in One Dimenston (New York: Academic)
McKellar B H J and Stephenson G J 1987 Phys. Rev. C 35 2262
MCndez B and Dominguez-Adame F 1991 1. Phys. A: Math Gen. 24 L331 - 1992 J. Phys. A: Moth. Gen. 25 2065
Roy C L and Bhattacharya K 1969 Indian J. Pure Appl. Phys. 7 306
Vigneron J P and Lambin Ph 1979 J. Phys. A: Mnfh. Gen. 12 1961