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Evaluation of the First Relaxed Excited State Energy of the Free Fröhlich Polaron
Author(s) -
Lépine Y.,
Charbonneau M.
Publication year - 1984
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.2221220117
Subject(s) - excited state , ansatz , polaron , gaussian , singularity , physics , ground state , atomic physics , quantum mechanics , chemistry , mathematics , mathematical analysis , electron
The first relaxed excited state energy of the free Fröhlich polaron is evaluated using the Fock approximation of Matz and Burkey. From a discussion of a variational‐type expression of this energy, it is concluded that a singularity in the space of variational parameters separates the ground state from the first relaxed excited state and that other singularities separate the other excited states. From this interpretation, this energy is evaluated, using two complete model spectra; a Gaussian spectrum and a second one involving an internal magnetic field in addition to the Gaussian part. It is found that for α ≦ 1.2 no excited state is observed. For 1.2 ≦ α ≦ 4.2, a two‐dimensional excited state is obtained while for α ≦ 4.2 a Gaussian excited state is obtained. These results are, however, limited by the choice of the model spectrum. For large α's, an asymptotic limit is obtained of ‐0.053α 2 ħω, a value close to that obtained from the best product ansatz calculations.