2004/01/01 by Nibaldo Alvarez-Moraga, Veronique Hussin, Véronique Hussin · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP
paper · pdf · doi:10.1023/b:ijtp.0000028859.11739.79
published as Inter. J. Theor. Phys. Vol. 43, N. 1 (2004) 179-218 · 42 pages
openalex publication_date 2004/01/01 · arxiv created 2005/04/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The superalgebra eigenstates (SAES) concept is introduced and then applied to find the SAES associated to the sh(2/2) superalgebra, also known as Heisenberg--Weyl Lie superalgebra. This implies to solve a Grassmannian eigenvalue superequation. Thus, the sh(2/2) SAES contain the class of supercoherent states associated to the supersymmetric harmonic oscillator and also a class of supersqueezed states associated to the osp(2/2) \sdir sh(2/2) superalgebra, where osp(2/2) denotes the orthosymplectic Lie superalgebra generated by the set of operators formed from the quadratic products of the Heisenberg--Weyl Lie superalgebra generators. The properties of these states are investigated and compared with those of the states obtained by applying the group-theoretical technics. Moreover, new classes of generalized supercoherent and supersqueezed states are also obtained. As an application, the superHermitian and η--pseudo--superHermitian Hamiltonians without a defined Grassmann parity and isospectral to the harmonic oscillator are constructed. Their eigenstates and associated supercoherent states are calculated.