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A Variational Method in Wannier Representation for an Electron Weakly Bound to an Isoelectronic Impurity
Author(s) -
Geistlinger H.,
Weller W.
Publication year - 1985
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221280237
Subject(s) - exciton , impurity , variational method , lattice (music) , space (punctuation) , electron , bound state , conduction band , wannier function , generalization , physics , quantum mechanics , upper and lower bounds , representation (politics) , chemistry , mathematics , mathematical analysis , politics , political science , law , philosophy , linguistics , acoustics
The problem of a single electron bound to an isoelectronic impurity (solved in k ‐space by Koster and Slater) is reconsidered in lattice space. An analytically tractable variational method for the ground state is developed and compared with the numerically evaluated solution in k ‐space. For GaP:N taking into account the real band structure of the lowest conduction band the variational method yields a sufficient agreement with the k ‐space eigenwert equation. The variational approach developed in the lattice space allows a straightforward generalization to the binding of an exciton (considered in I) which takes into account the electron‐hole correlation, crucially in the region of weak binding (e.g. GaP:N).