反常玻色产生算符的本征右矢

J4 ›› 2014, Vol. 31 ›› Issue (2): 135-140.

反常玻色产生算符的本征右矢

程建民,梁修东,朱正芳,吴卫锋,许业军

安徽省池州学院机械与电子工程系

收稿日期:2013-07-22 修回日期:2013-10-16 出版日期:2014-03-28 发布日期:2014-03-20
通讯作者: 许业军

Eigenkets of abnormal boson creation operator

Received:2013-07-22 Revised:2013-10-16 Published:2014-03-28 Online:2014-03-20

摘要/Abstract

摘要： 　鉴于反常玻色系统在相对论协变的零质量的矢量场中的重要地位和作用,利用Dirac函数的围道积分形式及其性质,并借助反常玻色系统粒子数表象的完备性特点,重点推导出了反常玻色产生算符的本征右矢具体的广义解形式,并在此基础上,寻找到与之对应的两组由非共轭反常玻色量子态矢构成的正交完备性关系,进一步发现此正交完备性关系并不与反常玻色系统中常出现的度规算符相关.最后,作为上述结论的应用,还推导出了量子力学和量子光学中经常出现的两个多项式（即:Hermite多项式和Laguerre多项式）的围道积分下的表示式,该表示形式具有普适性,可能对于解决有关以上两个多项式的量子光学问题提供帮助.

关键词: 围道积分

Abstract: Based on the important position and application of abnormal boson quantum system in the theory of relativistic covariant vector field of zero quality, the specific form of the eigenket of the abnormal boson creation operator can be derived by virtue of the contour integral representation of Dirac-function and its properties as well as the feature of the number representation of abnormal boson system. Furthermore, two sets of new orthogonality and completeness relations, which are irrelevant to normality operator, are obtained. Finally, as an applications, it is used to rewrite the expressions of the Hermite polynomial and Laguerre polynomial under the meaning of the contour integral, which presumably provide help for some questions of quantum optics about these polynomials.

Key words: contour integral

中图分类号:

O413.1

程建民梁修东朱正芳吴卫锋许业军. 反常玻色产生算符的本征右矢[J]. J4, 2014, 31(2): 135-140.

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