Pseudo-Boson Coherent and Fock States

Details Pseudo-Boson Coherent and Fock States Pseudo-Boson Coherent and Fock States

2009-02-21

arxiv.org/abs/0902.3744v1

in Differential Geometry, Complex Analysis and Mathematical Physics, eds. K. Sekigawa et al (W. Scientific 2009), pp. 241-250

Physics

Quantum Physics

10 pages, no figures. Based on talk given at 9th IC on Complex Structures, Integrability and Vector Fields, Sofia, August 2008

Scientific paper

Coherent states (CS) for non-Hermitian systems are introduced as eigenstates of pseudo-Hermitian boson annihilation operators. The set of these CS includes two subsets which form bi-normalized and bi-overcomplete system of states. The subsets consist of eigenstates of two complementary lowering pseudo-Hermitian boson operators. Explicit constructions are provided on the example of one-parameter family of pseudo-boson ladder operators. The wave functions of the eigenstates of the two complementary number operators, which form a bi-orthonormal system of Fock states, are found to be proportional to new polynomials, that are bi-orthogonal and can be regarded as a generalization of standard Hermite polynomials.

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