论文标题
$ q $ -Defformed相干状态与序列$ x_n^{q，α} =（1+αq^{n-1}）[n] _q $
$q$-deformed coherent states associated with the sequence $x_n^{q,α}=(1+αq^{n-1})[n]_q$
论文作者
论文摘要
我们通过更换$ [n] _q！$的$ q $ - Q $ - Q $ -C！$在经典$ q $ -cs的系列扩展中，通过概括$ x $ c $ q $ c $ x $ x_n^Q，q，q，α}！ $ x_n^{q，α} =（1+αq^{n-1}）[n] _q $。我们使用基于序列$ x_n^{q，α} $的移位运算符方法来获得实现Al-Salam-Chihara多项式的实现，以用于携带构建$ q $ -cs的Fock空间的基础向量。这些新状态在Arik-Coon类型的$ Q $ -CS（$α= 0 $，$ 0 <q <1 $）和一组Cooherent of Barut-Girardello类型的状态下，用于Meixner-Pollaczek振荡器（$α\ neq 0 $，$ q \ q \ to $ q \ to $ q \ to 1 $）。我们还讨论了它们相关的Bargmann类型变换。
We introduce new generalized $q$-deformed coherent states ($q$-CS) by replacing the $q$-factorial of $[n]_q!$ in the series expansion of the classical $q$-CS by the generalized factorial $x_n^{q,α}!$ where $x_n^{q,α}=(1+αq^{n-1})[n]_q$. We use the shifted operators method based on the sequence $x_n^{q,α}$ to obtain a realization in terms of Al-Salam-Chihara polynomials for the basis vectors of the Fock space carrying the constructed $q$-CS. These new states interpolate between the $q$-CS of Arik-Coon type ($α=0$, $0<q<1$) and a set of coherent states of Barut-Girardello type for the Meixner-Pollaczek oscillator ($α\neq 0$, $q\to 1$). We also discus their associated Bargmann type transforms.
