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Validity of Lee, Low and Pines Method in the Case of the Interaction of an Electron with a Single Lattice Oscillator
Author(s) -
Devreese J.,
Evrard R.
Publication year - 1963
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.19630031118
Subject(s) - lattice (music) , mean field theory , phonon , polaron , electron , physics , polarization (electrochemistry) , quantum mechanics , condensed matter physics , quantum electrodynamics , chemistry , acoustics
The LEE ‐ LOW ‐ PINES approximation (or LLP approximation) of polaron theory is applied to a model first studied by GROSS , in which the polarization field is supposed to have only one k ‐component. The results are compared with the exact solutions obtained with GROSS ' method. It is shown that, in the particular case of this model, the LLP approximation is not very satisfactory when the mean number of phonons is of the order of, or greater than, 1/2. Thus the relative smallness of the mean number of virtual phonons cannot provide an argument for the validity of the LLP method in the intermediate coupling region.