共查询到20条相似文献,搜索用时 78 毫秒
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研究表明,保证经典轨道具有封闭性的Bertrand定理可以进一步推广,在适当的角动量下,仍存在着非椭圆的闭合轨道.对于屏蔽Coulomb场,可获得广义Runge-Lenz矢量.这种轨道封闭性与径向Schr?dinger方程因式分解相对应. 相似文献
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对氢原子的径向Schrodinger方程,完全用因式分解方法,导出关于主量子数n和角量子数l的另外两类升降算子.用它们构造出第三类、第四类升降算子.并通过计算给出了四类升降算子的归一化系数. 相似文献
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N维氢原子的另外四类升降算子 总被引:1,自引:1,他引:0
从N维氢原子的径向Schrodinger方程出发,完全用因式分解方法,直接导出N(d≥2)维氢原子的另外第一类、第二类升降算子,并用这两类算子构造出新的第三类、第四类升降算子.当d=3和d=2时,得到三维与二维氢原子的升降算子和文献[5,7]中相同. 相似文献
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本文利用两种方法求解二维氢原子的径向方程:一是升降算符法,由所定义的关于量子数m的升降算符,给出了径向波函数之间的递推公式,求出了二维氢原子的能级和径向波函数的表达式;二是通过与三维氢原子径向方程的类比,在三维氢原子径向波函数的基础上,直接给出了二维氢原子径向波函数的一般表示式.两种解法所得结果完全一致. 相似文献
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四元数在建立波动方程中的应用 总被引:3,自引:3,他引:0
用四元数对经典的能量,动量关系式进行因式分解,建立起了现今人们已知的所有不同形式的波动方程,这样既表明了不同微观粒子不同的波动方程有着同一个来源,也为建立未知粒子的未知的波动方程提供了可能性。 相似文献
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可以用超对称量子力学方法[1] 很好地处理一维势阱能量正征值问题 ,这都受启于Schrodinger的一维谐振子的因式分解法和能量升、降算符的概念[2 ] ,在此借助因式分解法处理K—G方程 ,并将自然地得到Dirac方程 ,而且自然地说明其性质。 相似文献
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《Journal of Nonlinear Mathematical Physics》2013,20(3):299-309
The conserved quantities for the heated radial liquid jet and the heated radial free jet are established by using conservation laws. The flow in a heated radial jet is described by Prandtl's momentum boundary layer equation, the continuity equation and the energy equation. Viscous dissipation is neglected. The multiplier approach is used to derive the conservation laws for the system of three equations for the velocity components and the temperature and three conserved vectors are obtained. The conservation laws for the system of two partial differential equations for the stream function formulation are also computed by the multiplier approach and three conserved vectors are obtained. One of these is a non-local conserved vector for the system. The conserved quantities for the heated radial liquid jet and the heated radial free jet, emitted into a stationary fluid of uniform temperature θ∞, are derived by integrating the conservation laws across the jet. 相似文献
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Antonio Zecca 《International Journal of Theoretical Physics》2012,51(2):438-446
The spin 3/2 field equation is studied in the general Lema?tre–Tolman–Bondi (LTB) space-time. The equation is separated by
variable separation. The angular dependence factors out at the level of the general LTB metric. Due to spherical symmetry
the separated angular equations coincide with those, previously integrated, relative to the Robertson–Walker and Schwarzschild
metric. Separation of time and radial dependence is possible within a class of LTB cosmological models for which the physical
radius is a product of a time and a radial function, the last one being further selected by the consistency condition of the
radial equations. The separated time dependence, that can be integrated by series, results essentially unique. Instead the
radial dependence can be reduced to two independent second order ordinary differential equations that still depend on an arbitrary
radial function that is an integration function of the cosmological model. The generalization of the scheme to arbitrary spin
field equation is suggested. 相似文献
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Exact Solutions of the Klein-Gordon Equation with a New Anharmonic Oscillator Potential 总被引:2,自引:0,他引:2 下载免费PDF全文
We solve the Klein-Cordon equation with a new anharmonic oscillator potential and present the exact solutions. It is shown that under the condition of equal scalar and vector potentials, the Klein-Cordon equation could be separated into an angular equation and a radial equation. The angular solutions are the associated-Legendre polynomial and the radial solutions are expressed in terms of the confluent hypergeometric functions. Finally, the energy equation is obtained from the boundary condition satisfied by the radial wavefunctions. 相似文献
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Antonio Zecca 《International Journal of Theoretical Physics》2014,53(1):181-187
The problem of variable separation of the scalar field equation is approached within the Lemaître-Tolman-Bondi (LTB) cosmological model with cosmological constant Λ. Parametric solutions of the cosmological Newton-like equation of the model are preliminary determined that result factorized in the parameter and in the radial dependence. The result holds on a sufficient condition that relates the two arbitrary integration functions of the model. The condition is of the same type of the one that ensures, in absence of cosmological term, the separability of the spin field equations for spin 0, 1/2, 1. It is then shown that the scalar field equation results automatically separable in the class of LTB models determined. The separated radial equation results independent of Λ, while the separated time equation strictly depends on Λ. The separability of the field equations is then checked to hold, in the same context, for spinor field equation of spin 1/2 and spin 1. 相似文献
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N. K. Kofinti 《International Journal of Theoretical Physics》1984,23(10):991-999
By using the curved space-time Klein-Gordon equation, the form of the wave function of a scalar particle near a nonrotating black hole is obtained. It is shown that although the radial wave function oscillates infinitely rapidly near the black hole, the probability density remains finite even on the event horizon. This is consistent with the fact that the Schwarzschild surface is nonsingular. An expression is given for the large angular momentum scattering differential cross section by comparing the asymptotic form of the radial wave equation with the corresponding Coulomb radial wave equation in ordinary quantum mechanics. 相似文献
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利用反弹平均的三维Fokker-Planck方程,对电子回旋波加热和电流驱动进行数值模拟.考虑超热电子径向扩散对电流驱动的影响,在方程中加入径向扩散输运项,采用九点格式的中心差分对方程进行数值离散得到系数矩阵,采用不完全LU分解对系数矩阵进行预处理,利用双共轭梯度稳定法求解得到分布函数.在不考虑电子径向扩散输运条件下,得到电子回旋波驱动电流密度与功率沉积密度的分布;考虑径向扩散输运的计算结果与BANDIT3D进行比较,驱动电流分布的趋势基本一致. 相似文献
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Radial integrals, oscillator strengths, and polarizabilities of the thallium, lead and bismuth atoms
V. V. Flambaum O. P. Sushkov 《Journal of Quantitative Spectroscopy & Radiative Transfer》1978,20(6):569-579
The radial integrals for transitions of 6p-electrons to the excited states in the Tl, Pb and Bi atoms have been found by numerical integration of the Dirac equation with an effective potential. The radial integrals for excitation of 6s- and 5d-electrons from the closed subshells have been obtained from analysis of the available experimental data on the oscillator strengths in Tl, Hg, Au and the polarizability of Hg. Using these radial integrals, we determine the polarizabilities of the Tl, Pb and Bi atoms by a simple method that is similar to Sternheimer's method. 相似文献
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An anharmonic oscillatory potential is proposed in which a noncentral electric dipole is included. The pseudospin symmetry for this potential is investigated by working in a complete square integrable basis that supports a tridiagonal matrix representation of the wave operator. The resulting three-term recursion relation for the expansion coefficients of the wavefunctions (both angular and radial) are presented. The angular/radial wavefunction is written in terms of Jacobi/Laguerre polynomials. The discrete spectrum of the bound states is obtained by the diagonalization of the radial recursion relation. The algebraic properties of the energy equation are also discussed, showing the exact pseudospin symmetry. 相似文献
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对Schr?dinger方程引入修饰势,并将波函数展开为Floquet分波,即可实施分离变量。强光场时弱耦合法选取合适微扰量,径向波动方程可逐步近似求解。以圆极化强光场为例,计算了散射波函数、散射矩阵和截面。重要结论是:强光场下将出现多光子过程,对应m次多光子过程有相应的共振谱线族,谱线能量约为m?ω,并给出谱线强度计算公式。
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