共查询到18条相似文献,搜索用时 453 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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Wigner算符的正规乘积形式和相干态形式的应用 总被引:1,自引:0,他引:1
本文导出了Wigner算符的正规乘积形式和相干态形式及其若干应用, 其中包括若干新量子算符公式的导出, Moyal定理的相干态推广, 计算以前文献未曾得到的若干与经典函数对应的量子Weyl算符以及若干与量子算符对应的Weyl经典函数. 相似文献
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实空间中的概率流概念和概率守恒定理被推广到希尔伯特(Hilbert)状态空间,从而得到了概率流算符的通式.应用一般形式的概率流算符公式,还导出了紧束缚模型中单电子和互作用多电子系统的概率流算符,并以异常简单的方式证明了反射-透射流归一化条件
关键词:
希尔伯特空间
概率流算符
紧束缚模型 相似文献
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运用Wigner-Eckart定理可以把晶体场哈密顿算符表示为由角动量算符组成的等效算符,利用等效算符计算具有特定的J的耦合波函数之间的晶体场矩阵元特别方便,因为等效算符作用于耦合波函数的角度部份,不需要回到单电子波函数。 相似文献
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Fr. Debacker-Mathot 《Reports on Mathematical Physics》1977,11(3):361-375
We characterize the spectrum of the elements of some operator algebras acting in a nested Hilbert space. In one of those algebras we prove the spectral theorem for Hermitian operators and the SNAG theorem for unitary representations of locally compact Abelian groups. Then we extend the SNAG theorem to representations in three more general classes of operators. 相似文献
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The expansion theorem of quantum field theoy relating Heisenberg operators to asymptotic free-field operators is rewritten by means of the time-path technique, originally due to Schwinger, which to date has only found application in statistical mechanics. The theorem is combined with Bogoliubov's initial condition of vanishing correlations in the infinite past to rederive Keldysh's perturbation scheme for non-equilibrium statistical Green's functions. 相似文献
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J. Kutzner 《Zeitschrift für Physik A Hadrons and Nuclei》1973,259(2):177-188
We start with the definition of two mapping operators, one of them is the projection operator onto coherent spin states. With the help of these operators we derive a mapping theorem which defines a correspondence between the operators in spin space andc-number functions of a certain class. It is shown that this correspondence is one-to-one. The quantum-mechanical expectation value of an operator is found to be expressible in the form of a phase space average of classical statistical mechanics. We also derive a product theorem which allows us to transcribe the equations of motion for operators into equivalent equations for thec-number functions. As an illustration of the theory, some examples are discussed. 相似文献
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A.U. Klimyk 《Reports on Mathematical Physics》1975,7(2):153-166
The Wigner-Eckart theorem for matrix elements of tensor operators transforming according to a finite-dimensional representation of a non-compact semisimple Lie group is proved. The applications of this theorem are discussed. 相似文献
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We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate η-invariants and prove an APS theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities. 相似文献
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Masuo Suzuki 《Communications in Mathematical Physics》1994,163(3):491-508
A general theorem is proved concerning the convergence of decompositions of exponential operators in a Banach space (or normed space). As a corollary, the convergence of fractal decompositions is proved. The convergence of generalized. Trotter-like formulas is also shown to result from the general theorem. 相似文献
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陈刚 《原子与分子物理学报》2003,20(1):89-91
运用升降算子和超维里定理计算出原子模型势中任意算符Af^U2(r)的矩阵元〈n′1l′1|Af^U2(r)|n1l1〉的递推关系. 相似文献
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P. A. Rejto 《Letters in Mathematical Physics》1976,1(2):111-118
We study the resolvents of a specific family of nonself-adjoint operators. This family of non-self-adjoint operators played a role in the proof of an extended version of a theorem of Titchmarsh-Neumark-Walter concerning absolutely continuous operators. We make essential use of the JWKB-approximation method. 相似文献