Pseudo-Hermitian coherent states under the generalized quantum condition with position-dependent mass
arXiv:1201.2372 · doi:10.1088/1751-8113/45/44/444034
Abstract
In the context of the factorization method, we investigate the pseudo- Hermitian coherent states and its Hermitian counterpart coherent states under the generalized quantum condition in the framework of a position-dependent mass. By considering a specific modification in the superpotential, a suitable annihilation and creation operators are constructed in order to reproduce the Hermitian counterpart Hamiltonian in the factorized form. We show that by means of these ladder operators we can construct a wide kind of exactly solvable potentials as well as their accompanying coherent states. Alternatively, we explore the relationship between the pseudo-Hermitian Hamiltonian and its Hermitian counterparts, obtained from a similarity transformation, to construct the associated pseudo-Hermitian coherent states. These latter preserve the structure of Perelomov's states and minimize the generalized position-momentum uncertainty principal.
14 pages
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- Position-dependent mass, finite-gap systems, and supersymmetry
- Coherent and squeezed states: introductory review of basic notions, properties and generalizations
- Position-dependent mass systems: Classical and quantum pictures
- Isospectral Hamiltonian for position-dependent mass for an arbitrary quantum system and coherent states
- Complementarity versus coordinate transformations: mapping between pseudo-Hermiticity and weak pseudo-Hermiticity