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This article is cited in 9 scientific papers (total in 9 papers)
Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
Omar Cherbala, Mahrez Drira, Mustapha Maamacheb, Dimitar A. Trifonovc 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
Abstract:
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 $H=\omega J_3+\alpha J_{-}+\beta J_+$, $\alpha\neq\beta$, 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.
Keywords:
pseudo-Hermitian quantum mechanics; supersymmetry; supercoherent states.
Received: September 29, 2010; in final form December 4, 2010; Published online December 15, 2010
Citation:
Omar Cherbal, Mahrez Drir, Mustapha Maamache, Dimitar A. Trifonov, “Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States”, SIGMA, 6 (2010), 096, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma554 https://www.mathnet.ru/eng/sigma/v6/p96
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