Trions in first and second quantizations

European Physical Journal B

Volumn 33, Issue 3, 2003, Pages 311-320

  Combescot, Monique ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EXCITONS; FREE ELECTRON LASERS; MATHEMATICAL OPERATORS;

QUANTIZATION; SEMICONDUCTOR TRIONS;

SEMICONDUCTOR MATERIALS;

EID: 0141804348     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2003-00171-x     Document Type: Article

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25. While the energies and wave functions in 3D and 2D are of course correct, the usual resolution of the Schrödinger equation, as found for example in Landau-Lifshitz, Quantum mechanics, is mathematically inconsistent as it relies on two hypergeometric functions which are accidentally proportional for the parameters of physical interest. As a dramatic consequence, the proposed resolution cannot be extended to ID excitons. See M. Combescot, submitted to Solid State Com.
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27. e′ play similar rôles and which fulfil equations (12, 14). They are however less convenient than our (r, u′) for the extension of this work to one hole plus 3,4,5. . . electrons
28. The variables (R, r) used by Thiligam (Ref. (6)) are nothing but our variables (r, u′). We however do not see why his r and R have to be colinear, as stated in his equation (13), even for 2D trions
29. In this paper, we have dropped all band gaps Δ. The exciton energy as well as the free electron energy should have an additional Δ, while the trion energy should have an additional 2Δ This in fact implies to add a 2Δ to the RHS of the Hamiltonian given in equation (1). In equation (49) however, these Δ are unimportant since they cancel