Differential Realizations of the Two-Mode Bosonic and Fermionic Hamiltonians: A unified Approach

Details Differential Realizations of the Two-Mode Bosonic and Fermionic Hamiltonians: A unified Approach Differential Realizations of the Two-Mode Bosonic and Fermionic Hamiltonians: A unified Approach

2004-10-10

arxiv.org/abs/math-ph/0410025v1

PRAMANA J. Phys. V62 2004 993-1005

Physics

Mathematical Physics

Scientific paper

A method is developed to determine the eigenvalues and eigenfunction of two-boson $2\times 2$ matrix Hamiltonians include a wide class of quantum optical models. The quantum Hamiltonians have been transformed in the form of the one variable differential equation and the conditions for its solvability have been discussed. We present two different transformation procedure and we show our approach unify various approaches based on Lie algebraic technique. As an application, solutions of the modified Jaynes-Cummings and two-level Jahn Teller Hamiltonians are studied.

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