Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 096, 11 pages      arXiv:1009.5293
Contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”

Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States

Omar Cherbal a, Mahrez Drir a, Mustapha Maamache b and Dimitar A. Trifonov c
a) Faculty of Physics, Theoretical Physics Laboratory, USTHB, B.P. 32, El Alia, Algiers 16111, Algeria
b) Laboratoire de Physique Quantique et Systemes Dynamiques, Department of Physics, Setif University, Setif 19000, Algeria
c) Institute of Nuclear Research, 72 Tzarigradsko chaussée, 1784 Sofia, Bulgaria

Received September 29, 2010, in final form December 04, 2010; Published online December 15, 2010

A new class of non-Hermitian Hamiltonians with real spectrum, which are written as a real linear combination of su(2) generators in the form HJ3JJ+, α≠β, is analyzed. The metrics which allows the transition to the equivalent Hermitian Hamiltonian is established. A pseudo-Hermitian supersymmetic extension of such Hamiltonians is performed. They correspond to the pseudo-Hermitian supersymmetric systems of the boson-phermion oscillators. We extend the supercoherent states formalism to such supersymmetic systems via the pseudo-unitary supersymmetric displacement operator method. The constructed family of these supercoherent states consists of two dual subfamilies that form a bi-overcomplete and bi-normal system in the boson-phermion Fock space. The states of each subfamily are eigenvectors of the boson annihilation operator and of one of the two phermion lowering operators.

Key words: pseudo-Hermitian quantum mechanics; supersymmetry; supercoherent states.

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