Abstract
We consider the Hartree equations for a system of an infinite number of electrons in a periodic potential consisting of a periodic array of wells. The filling fraction is assumed to be of one electron per well. We prove that if the wells are deep enough to admit a bound state and if they are separated by a distance large enough, then the Hartree equations have a solution in which all single particle wave functions decay exponentially.
Similar content being viewed by others
References
Mott, N.: Metal-insulator transitions, London: Taylor & Francis 1974
Albanese, C.: ETH preprint 1988
Albanese, C.: A continuation method for non-linear eigenvalue problems. J. Funct. Anal. (to appear)
Reed, M., Simon, B.: Methods of modern mathematical physics. New York: Academic Press 1979
Glimm, J., Jaffe, A.: Quantum physics. Berlin, Heidelberg, New York: Springer 1981
Author information
Authors and Affiliations
Additional information
Communicated by C. H. Taubes
Rights and permissions
About this article
Cite this article
Albanese, C. Localised solutions of Hartree equations for narrow-band crystals. Commun.Math. Phys. 120, 97–103 (1988). https://doi.org/10.1007/BF01223207
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01223207