反WKB方法的改进

改进了用于确定渐变平面波导折射率分布的反WKB方法。这种渐变折射率分布是从在WKB近似的条件下得到的本征方程用数值方法求得的。用改进的反WKB方法计算3种(指数、高斯和阶跃函数)折射率分布，结果验证了该方法的有效性。先用最小二乘法拟合测量得到的有效折射率。进而求出有效折射率函数，再利用改进的算法分布计算出各自的折射率分布。计算结果同精确值吻合得很好。计算出的波导表明折射率同精确值的绝对误差约为0．1%。     

改进WKB方法与相移值的修正

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。     

变波长逆WKB方法确定单模渐变平面光波导的折射率轮廓

将渐变波导模式方程(WKB积分方程)化为分段积分,以波导某一模式在不同波长下的转折点为分段点,当波长相差很小时,相应的转折点相差也很小,可在各个分段积分中作折线近似,从而从理论上推出确定波导轮廓数据的递推式.以所得轮廓必须满足光滑条件为判据,最后定出波导的轮廓.该方法尤其适用于单模渐变波导,而且无需事先假设待定轮廓的函数形式.本文对双曲止割和抛物线轮廓的理想波导进行了计算机模拟,结果证明该方法的精度达到10~(-3)甚至于更高.而且理论上具有分割愈密,精度愈高的优点.     

WKB波函数连接公式的初等推导与一维势阱势垒的WKB近似解

本文用初等方法导出ＷＫＢ波函数的连接公式，其要点是在转折点邻近，用阶跃型势能曲线代替真实的势能曲线。给出了求一维势阱能级及一维势垒穿透因子的方法与结果。方法简便，可供初等量子力学与普通物理教学参考。     

确定介质波导导模折射率的一种新方法

介绍一种确定平面介质波导导模折射率的新法，它是Ｒｕｓｃｈｉｎ－Ｌｉｔ计模法的推广，与计模法有关的半相位移关系得到完善，本文还给出新法在几种有代表性波导中的应用和计算结果。     

多层介质波导的一种新方法及其在非均匀介质平面光波导中的应用

本文提出求解多层介质平面光波导的一个简单而直接的方法。将其应用于非均匀平面光波导,可以求解任意折射率分布和TM模问题。以抛物线型和指数型分布为例,说明只要分层数目足够多,本文介绍的方法可以达到任意精度。     

用科尔-霍普夫变换法求非均匀光波导导模本征方程的严格解

采用科尔-霍普夫(Cole-Hopf)变换法，将渐变折射率波导导模的本征值方程变换为里卡提(Riccati)方程，通过较简洁的数学演算导出导模的传播常量与模场分布的解析解，给出了平方律分布、对称爱泼斯坦(Epstein)分布、爱泼斯坦层的平板波导与平方律分布圆光纤4种折射率分布的计算公式。     

高斯光束在梯度折射率纤维中的传播—振幅与光斑分布的解析解族

从近轴波动方程出发，导出在梯度折射率纤维中传播的高斯光束振幅与光斑分布的解析解族。从这一结果可得到高斯光束在抛物型、锥形、类锥形梯度折射率纤维中传播的一系列特解。     

WKB近似方法在解对称四次方双势阱中的应用

利用ＷＫＢ近似方法求解对称四次方双势阱问题并对结果进行了讨论。     

Quantization of Higher-Order Constrained Lagrangian Systems Using the WKB Approximation

A general theory is given for solving the Hamilton–Jacobi partial differential equations (HJPDEs) for both constrained and unconstrained systems with arbitrarily higher-order Lagrangians. The Hamilton–Jacobi function is obtained for both types of systems by solving the appropriate set of HJPDEs. This is used to determine the solutions of the equations of motion. The quantization of both systems is then achieved using the WKB approximation. In constrained systems, the constraints become conditions on the wave function to be satisfied in the semiclassical limit.     

Quantization of Christ—Lee Model Using the WKB Approximation

The Hamilton-Jacobi formalism for constrained systems is applied to the Christ-Lee model. The equations of motion are obtained and the action integral is determined in the configuration space. This enables us to quantize the Christ-Lee model by using the WKB approximation.     

Notes on Application of WKB Method

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.     

Notes on Application of WKB Method

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.     

Supersymmetric WKB Approximation of Anharmonic Potential V(r)=ar2+br-4+cr-6

This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V(r) = ar2 br-4 cr-6 in order to tesify the correctness between [Phys.Lett. A 170 (1992) 335] and the paper written by M. Landtman [Phys. Lett. A 175 (1993) 147].     

Supersymmetric WKB Approximation of Anharmonic Potential V（r）=ar^2＋br^-4＋cr^-6

This article uses the supersymmetric WKB approximation to obtain the approximate energy levels and wave functions of the anharmonic potential V（r） = ar^2 ＋ br^-4 ＋ cr^-6 in order to tesify the correctness between [Phys. Left. A 170 （1992） 335] and the paper written by M. Landtman [Phys. Left. A 175 （1993） 147].     

超对称准经典近似和本征值问题

运用超对称准经典近似方法给出三维谐振子、氢原子的能谱,进而将该方法用于含角坐标的二阶微分方程,得到角动量平方L2的本征值和非中心势的角向本征值.     

WKB approximation in complex time

The WKB approximation to the one particle Schrödinger equation in time is used to obtain the wavefunction at a given point as a sum of semiclassical terms, each corresponding to a different classical trajectory (real or complex) but ending up at the same point. A method to find out reflection coefficient for processes involving one and two turning points is developed and it is shown that the semiclassical complex analysis reproduces exactly the reflection coefficient that is obtained through the exact solution of the problem. The connection between pair production and reflection amplitude is also shown. The pair production amplitude in a time dependent gravitational background is calculated and it is shown that the vacuum considered in complex trajectory WKB analysis refers to adiabatic vacuum.