共查询到20条相似文献,搜索用时 109 毫秒
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各向同性谐振子是量子理论中能够严格求解的可解势场之一.对它的研究和讨论,在理论上和实际的应用中都有重要意义.本文推导出了N维(N≥2)各向同性谐振子径向矩阵元〈nrl|rk|nr′l′〉的递推公式,在此基础上得到了平均值的递推公式,并且讨论了维各向同性谐振子径向矩阵元的递推公式的一般性,而文献[3]与[4]所给出的各向同性谐振子径向矩阵元的递推公式只是本文结论的特例. 相似文献
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推导出三维各向同性谐振子径向矩阵元〈nl|rp|n′l′〉所满足的递推关系
关键词: 相似文献
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给出了相对论性无自旋氢原子的解析波函数,推导出了计算径向矩阵元的通项公式.在-6≤s≤3的条件下,给出了径向平均值〈n′l′|rs|n′l′〉的解析表达式. 相似文献
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根据广义Laguerre多项式的数学性质,导出了较为简单的三维各向同性谐振子径向矩阵元的普遍公式,并在这基础上计算了一些重要特殊情形的径向矩阵元: 矢径r整数次幂的平均值,电偶极跃迁矩阵元和电四极跃迁矩阵元.
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三维各向同性谐振子
径向矩阵元
广义Laguerre多项式
偶极跃迁
四极跃迁 相似文献
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Various equations for tc obtained from approximations to the Eliashberg theory are numerically solved and Tcvs λ curves are drawn. Specifically, the weak coupling Kirzhnits, Maksimov and Khomskii (KMK) equation, Eliashberg equation and BCS equation with Bardeen Pines interaction are considered with the α2F function of Nb. The KMK equation gives quite a high value or Tc and the BCS equation overestimates Tc by an even larger factor when compared with the results of the Eliashberg equation. 相似文献
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I. V. Sokolov 《Journal of Experimental and Theoretical Physics》2009,109(2):207-212
Dirac’s analysis of radiation reaction force in classical electrodynamics suggested that a 4-momentum not collinear with 4-velocity
could be introduced for a radiating electron. This would be equivalent to renormalization of the electron mass as an operator
relating these 4-vectors. Dirac also pointed to an arbitrary choice made in deriving the Lorentz-Abraham-Dirac (LAD) equation.
It was shown that renormalization substantially modifies the LAD equation under the additional requirement that the standard
relativistic relation ℰ2 = p
2
c
2 + m
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c
4 holds for the renormalized energy and momentum. The renormalized LAD equation is more rigorous than the LAD equation, because
the drawbacks of the latter are eliminated, and is simpler than a well-known approximation of the LAD equation. The renormalized
LAD equation appears to be better suited for numerical simulations of processes in ultrahigh-intensity laser-pulse fields. 相似文献
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M. Carmeli 《Foundations of Physics》1985,15(2):175-184
A Klein-Gordon-type equation onR×S
3 topology is derived, and its nonrelativistic Schrödinger equation is given. The equation is obtained with a Laplacian defined onS
3 topology instead of the ordinary Laplacian. A discussion of the solutions and the physical interpretation of the equation are subsequently given, and the most general solution to the equation is presented. 相似文献
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A more general relativistic Vlasov equation has been derived in the framework of relativistic quantum hadron dynamical theory. In the small amplitude limit we use this Vlasov equation to study the isovector giant dipole resonances built on groundstate in spherical nuclei16O,40Ca,90Zn and208Pb. The results show that the spin-orbit coupling and the non-linear terms of scalar meson can influence the resonance energies to a certain extent comparing with those obtained from the non-relativistic Vlasov equation approach and are in good agreement with the experimental ones, especially for the case which vacuum fluctuation is included. 相似文献
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A. A. Belov N. N. Kalitkin I. A. Kozlitin K. I. Lutskiy 《Bulletin of the Russian Academy of Sciences: Physics》2017,81(1):55-59
A plasma equation of state in a gas domain is derived from Saha model accounting for ion cores. Calculations for Cu are performed using the stiff ion core model for densities of up to 106 g/cm3. A compressible ion core model is also developed. The Tomas–Fermi model is applied to condensed plasma. Both models are unified into a thermodynamically consistent equation of state. 相似文献
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The observation that the soliton-like solutions of a given second-order nonlinear differential equation define the separatrix of the equivalent autonomous system is used to obtain the one-soliton solutions for theφ 4 theories (the usual and the one with the wrong sign of the mass term), theφ 6, theφ 8, the sine-Gordon theories and the KdV equation. Transformations are given which transform the sine-Gordon equation into an equation belonging to theφ 2n class of theories. A procedure is evolved for obtaining the two-soliton solutions for the sine-Gordon theory without the use of Backlund transformations; it is suggested that this procedure may be useful for investigating the existence of similar solutions for theories of the polynomial type. 相似文献
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Ruan Tu-nan et al. [1] have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limitM 2→∞ in the ladder approximation of single photon exchange. We show that up to orderO(α4) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of orderO(α6). 相似文献