Ordering positive and negative exponential power operators by virtue of special functions and analogy method
Ordering positive and negative exponential power operators by virtue of special functions and analogy method
研究算符函数的有序化排列是一项重要的数理任务. 本文利用特殊函数和正规乘积排序与反正规乘积排序间的互换法则法导出了幂算符<inline-formula><tex-math id="M1">\begin{document}$ {\left(a{a}^\dagger \right)}^{\pm n} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M1.png"/></alternatives></inline-formula>和<inline-formula><tex-math id="M2">\begin{document}$ {\left({a}^\dagger a\right)}^{\pm n} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M2.png"/></alternatives></inline-formula>的正规与反正规乘积排序. 进一步, 利用类比法得到了算符<inline-formula><tex-math id="M3">\begin{document}$ {\left(XP\right)}^{\pm n} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M3.png"/></alternatives></inline-formula>和<inline-formula><tex-math id="M4">\begin{document}$ {\left(PX\right)}^{\pm n} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20201652_M4.png"/></alternatives></inline-formula>的坐标-动量排序与动量-坐标排序式. 最后, 对新得到的这些算符结果的应用进行一些讨论.