共查询到16条相似文献,搜索用时 93 毫秒
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提出量子力学算符Hermite多项式方法,即将若干常用的特殊函数的宗量由普通数变为算符,并用它来发现涉及Hermite多项式(单变数和双变数)的二项式定理和涉及Laguerre多项式的负二项式定理,它们在计算若干量子光场的物理性质时有实质性的应用. 该方法不但具有简捷的优点,而且能导出很多新的算符恒等式,成为发展数学物理理论的一个重要分支.
关键词:
量子力学
Hermite多项式
二项式定理
Laguerre多项式 相似文献
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强调双模厄米多项式在量子光学理论中的地位,认为它是研究连续变量纠缠态和压缩态的必要函数,具有明确的物理意义。利用双模厄米多项式,结合有序算符内的积分技术,给出了若干新的算符恒等式和互逆的积分变换公式,证明了压缩双模粒子数态恰好是双变量厄米多项式激发压缩真空态。 相似文献
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在量子光学理论计算中,经常遇到算符的正规排序和反正规排序问题,我们从双变量厄米多项式Hm,n(x,y)的母函数出发,导出两个简洁的重要的基本算符恒等式并由此可以给出一些推论公式。 相似文献
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Multivariable generalizations of the classical Hermite, Laguerre and Jacobi polynomials occur as the polynomial part of the
eigenfunctions of certain Schr?dinger operators for Calogero-Sutherland-type quantum systems. For the generalized Hermite
and Laguerre polynomials the multidimensional analogues of many classical results regarding generating functions, differentiation
and integration formulas, recurrence relations and summation theorems are obtained. We use this and related theory to evaluate
the global limit of the ground state density, obtaining in the Hermite case the Wigner semi-circle law, and to give an explicit
solution for an initial value problem in the Hermite and Laguerre case.
Received: 16 August 1996 / Accepted: 21 January 1997 相似文献
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Guoquan Zhou 《Optics & Laser Technology》2012,44(1):218-225
Based on the vector angular spectrum method and the method of stationary phase, an analytical expression for the vectorial structure of the far field of an elegant Hermite–Gaussian beam is derived. The analytical formulae of the energy flux distributions of the TE term, the TM term, and the whole beam are presented in the far field. Analytical expressions for the ratios of the powers of the TE and TM terms to those of the elegant Hermite–Gaussian beam are obtained without any approximation. The physical pictures of the far field of an elegant Hermite–Gaussian beam are demonstrated and compared with those of the far field of the corresponding standard Hermite–Gaussian beam. This research reveals the internal vectorial structure of the far field of an elegant Hermite–Gaussian beam from an alternative viewpoint. 相似文献
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Based on the vectorial structure of electromagnetic beam and the
method of stationary phase, the analytical structure of Hermite
Gaussian beam in far field is presented. The structural energy flux
distributions are also investigated in the far field. The structural
pictures of some Hermite Gaussian beams are depicted in the far
field. As the structure of Hermite Gaussian beam is dominated by the
transverse mode numbers and the initial transverse Gaussian half
width, it is more complex than that of Gaussian beam. The ratios of
the structural energy fluxes to the whole energy flux are independent
of the transverse mode numbers and the initial transverse Gaussian
half width.
The present research reveals the internal vectorial structure of Hermite Gaussian beam from other viewpoint.\ 相似文献
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With the help of technique of integration within an ordered product (IWOP) of operators we find new integration transformation connecting the coherent state and the biparticle entangled state. We also point out that under this kind of integration transformation the direct product of two single-variable Hermite polynomials behaves quite different from the two-variable Hermite polynomials, in this way we show that the latter is intrinsic to the phase space of quantum entanglement. As a byproduct, some operator identities for theoretical quantum optics can also be neatly expressed in terms of the two-variable Hermite polynomials. 相似文献
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The nonclassicality of the two-variable Hermite polynomial state is investigated. It is found that the two-variable Hermite polynomial state can be considered as a two-mode photon subtracted squeezed vacuum state. A compact expression for the Wigner function is also derived analytically by using the Weyl-ordered operator invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of the Wigner function. Then violations of Bell’s inequality for the two-variable Hermite polynomial state are studied. 相似文献