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改进WKB方法与相移值的修正 总被引:4,自引:0,他引:4
利用非均匀波导的多层分割法,对传统WKB法的相称值进行修正,导出了改进的WKB计算公式,并给出相移修正值的计算公式。对常见的典型折射率剖面(指数型、高斯型、余误差型、截断线型)的数值计算表明,该方法所得公式的精度远高于传统的WKB近似,在接近截止时仍与精确数值十分吻合。 相似文献
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基于等效衰减矢方法的非均匀光波导色散方程 总被引:1,自引:0,他引:1
利用转换矩阵理论和等效衰减矢的概念,以此为根据分析了任意折射率分布平板波导的模式传输特性,导出了意义明确的非均匀平板波导的色散方程的严格的解析解,并指出了WKB法的局限性,数值计算的结果表明本文所得公式的结果和严格的数值解非常接近,表明本文所得的公式是严格的。 相似文献
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本文将W.K.B近似法拓宽到缓变参量条件下的计算,类比了量子理论中的结果,并就渐变折射率光波导和平面分层介质两种模型为例做了探讨。 相似文献
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克尔型非线性薄膜波导的TE模 总被引:4,自引:1,他引:3
对于芯区为克尔型非线性介质,覆盖层和衬底为线性介质的平板波导,用Krylov-Bogoliubov-Mitropolsky的渐近法导出了色散方程及场分布的二阶近似数学表达式,计算量大为减少且结果精确。给出了对称和非对称情况的典型实例。 相似文献
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改进WKB近似的新方法 总被引:4,自引:2,他引:2
利用转移矩阵理论,在考虑层间一次反射和转折点处实际相移的基础上,导出了改进的WKB公式,数值计算的结果表明本文所得公式的精度远优于传统的WKB近似,而且能适用于接近于截止的模式和变化剧烈的折射率分布。 相似文献
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本由WKB方法和玻尔-索末菲量子化规则,求出了无限深球方势阱中粒子能级近似满足的超越方程;然后通过进一步近似,找到了粒子能级近似满足的解析式并对所得结果的精度进行了计算机分析。 相似文献
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Asiri Nanayakkara 《理论物理通讯》2004,42(11)
A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V (x) = xN. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x) = x4 iAx are obtained. These zeros exhibit complex version of interlacing. 相似文献
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AsiriNanayakkara 《理论物理通讯》2004,42(5):693-698
A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V(x)=x^N. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x)=x^4 iAx are obtained. These zeros exhibit complex version of in terlacing. 相似文献
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N. I. Zhirnov 《Russian Physics Journal》1966,9(5):25-28
The nature and the conditions of applicability of the generalized WKB method (the Petrashen-Miller-Good method) are investigated. It is shown that the generalized WKB method is a new approximate method for quantum mechanics, differing essentially from the WKB method.In conclusion I wish to express my sincere appreciation to Academicians V. A. Fok and M. I. Petrashen for their interest in this work and their valuable advice in the process of its completion. 相似文献
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R. Rajaraman 《Physics Reports》1975,21(5):227-313
A pedagogical introduction is given to non-perturbative semi-classical methods for finding solutions to quantum field theories. Both the weak coupling method based on a time-independent classical solution, and the WKB method based on all periodic orbits are developed in detail, proceeding ffrom elementary quantum mechanics to field theory in stages. Both methods are then illustrated in model field theories. The [λø4]2 theory to which the weak coupling method is applied yields a new family of “kink” states whose properties are discussed.The WKB method is illustrated by quantizing “soliton” and “doublet” solutions of the two-dimensional sine-Gordon theory. The results are compared to consequences of Coleman's equivalence proof relating this system to the massive Thirring model. The speculation that solitons may be fermions is discussed, along with indications that the WKB method may ne yielding exact mass ratios for this theory.A final section is devoted to solutions of more realistic four-dimensional models containing fermions, internal symmetry etc. Some quark-confinement models and vortex type solutions come under this category. General remarks are made on this family of solutions, and illustrated using 't Hooft's monopole solution. 相似文献
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We use Wentzel–Kramers–Brillouin (WKB) approximation for calculating the slope and curvature of Isgur–Wise function in a QCD-inspired potential model. This work is an extension of the approximation methods to the QCD-inspired potential model. The approach hints at an effective range of distance for calculating the slope and curvature of Isgur–Wise function. Comparison is also made with those of Dalgarno method and variationally improved perturbation theory (VIPT) as well as other models to show the advantages of using WKB approximation. 相似文献
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The notes here presented are of the modifications introduced in
the application of WKB method. The problems of two- and
three-dimensional harmonic oscillator potential are revisited by WKB and
the new formulation of quantization rule respectively. It is found
that the energy spectrum of the radial harmonic oscillator, which
is reproduced exactly by the standard WKB method with the Langer
modification, is also reproduced exactly without the Langer
modification via the new quantization rule approach. An
alternative way to obtain the non-integral Maslov index for
three-dimensional harmonic oscillator is proposed. 相似文献
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We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections. 相似文献
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V. V. Rubish V. Yu. Lazur O. K. Reity S. Chalupka M. Salak 《Czechoslovak Journal of Physics》2004,54(9):897-919
The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The
relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For
spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogen-like atom is calculated.
Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done. 相似文献
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Ag+-Na+ and K+-Na+ ion-exchanged optical waveguides in soda-lime glass are characterised by ellipsometry. Refractive index profiles of the waveguides are calculated from ellipsometric multiple angle of incidence data using the Newton-Kantorovitch type iterative procedure and compared with those reconstructed by inverse WKB method. It is demonstrated that such continuous profiles with relatively small index gradient (of the order of 0.1 and 0.01), extending to few micrometers in depth, can be determined by ellipsometric measurements. A good agreement is found between results obtained by ellipsometry and by the inverse WKB method at depths above 500–600 nm, while there is a difference in the subsurface region, where ellipsometry is more sensitive to the quality of the surface. The profiles obtained by the two methods are consistent if the surface thin layer is etched. 相似文献