Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials
Generalized coherent states for oscillators connected with Meixner and Meixner—Pollaczek polynomials
复制标题
与 Meixner 和 Meixner-Pollaczek 多项式相关的振荡器的广义相干态
DOI：
10.1007/s10958-006-0182-y
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发表时间：
2006
影响因子：
--
通讯作者：
E. Damaskinsky
中科院分区：
文献类型：
--
作者：
V. Borzov;E. Damaskinsky
作者继续研究与给定的正交多项式族相关的类振荡器系统的广义相干态。在这项工作中，我们考虑与 Meixner 和 Meixner-Pollaczek 多项式相关的振荡器，并为这些振荡器定义广义相干态。这些状态的完备性条件是通过解决相关的经典矩问题来证明的。结果与其他作者的结果进行了比较。特别是，我们证明了线性谐振子相对论模型的哈密顿量可以被视为二次哈密顿量的线性化，这在我们的形式主义中自然出现。参考书目：56 种。
The authors continue to study generalized coherent states for oscillator-like systems connected with a given family of orthogonal polynomials. In this work, we consider oscillators connected with Meixner and Meixner— Pollaczek polynomials and define generalized coherent states for these oscillators. A completeness condition for these states is proved by solution of a related classical moment problem. The results are compared with the other authors ones. In particular, we show that the Hamiltonian of the relativistic model of a linear harmonic oscillator can be treated as the linearization of a quadratic Hamiltonian, which arises naturally in our formalism. Bibliography: 56 titles.