Realizations of the osp (2,1) superalgebra and related physical systems

Eigenvalues and eigenfunction of two-boson 2x2 Hamiltonians in the framework of the superalgebra osp(2,1) are determined by presenting a similarity transformation. The Hamiltonians include two bosons and one fermion have been transformed in the form of the one variable differential equations and the...

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Bibliographic Details
Published in:Turkish journal of physics 2004, Vol.28 (3), p.145-153
Main Authors: TÜTÜNCÜLER, Hayriye, KOÇ, Ramazan
Format: Article
Language:English
Subjects:
Benzerlik
boson
Bozon
eigenfunction
eigenvalue
Jaynes-Cummings model
Jaynes-Cummings modeli
Matematik
Mathematics
Nuclear Physics
Nükleer Fizik
similarity
superalgebra
Süper cebir
Özdeğer
Özfonksiyon
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Summary:Eigenvalues and eigenfunction of two-boson 2x2 Hamiltonians in the framework of the superalgebra osp(2,1) are determined by presenting a similarity transformation. The Hamiltonians include two bosons and one fermion have been transformed in the form of the one variable differential equations and the conditions for its solvability have been discussed. It is observed that the Hamiltonians of the various physical systems can be written in terms of the generators of the osp(2,1) superalgebra and under some certain conditions their eigenstates can exactly be obtained. In particular, the procedure given here is useful in determining eigenstates of the Jaynes-Cummings Hamiltonians.
ISSN:1300-0101