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发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrdinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高.
关键词:
三维含时Schrdinger方程
库仑奇点
强场
含时波包传播 相似文献
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本文通过数值求解动量空间的三维含时薛定谔方程, 研究了原子高激发态在高频激光脉冲作用下, 在电离阈值附近的光电子能谱和两维动量角分布. 研究结果表明: 在该能量范围内, 单光子电离过程的贡献是最主要的. 体系初态的主量子数可以由光电子能谱峰值的位置来确定; 体系初态的角量子数可以通过光电子的两维动量角度分布确定. 在比较宽泛的参数范围内, 这一规律不随入射激光的强度和脉冲时间宽度的改变而改变, 因此原则上可以利用它对原子的初态进行识别. 此外, 还研究了体系的初态为相干叠加态, 光电子动量谱随着叠加态相对相位的变化规律.
关键词:
阈上电离
激发态
高频激光脉冲
两维动量角度分布 相似文献
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基于Dirac-slater自洽场方法,本文计算了C元素各价离子从低能到高能的光电离截面,考察了多极效应、相对论效应在不同能区对光电离截面的影响,并研究了光电离截面随光子能量、电离度、不同壳层变化的规律.通过各种理论计算结果的比较,分析了Kramers公式的适用性,计算中为了提高计算精度,我们采用了Grasp2程序包输出的束缚态波函数替换自洽场的波函数。 相似文献
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We systematically investigate the influence of atomic potentials on the above-threshold ionization (ATI) spectra in one-dimensional (1D) cases and compare them with the three-dimensional (3D) case by numerically solving the time-dependent Schrrdinger equation. It is found that the direct ionization plateau and the rescattering plateau of the ATI spectrum in the 3D case can be well reproduced by the 1D ATI spectra calculated from the supersolid-core potential and the soft-core potential, respectively. By analyzing the factors that affect the yield of the ATI spectrum, we propose a modified-potential with which we can reproduce the overall 3D ATI spectrum. In addition, the influence of the incident laser intensities and frequencies on the ATI spectra calculated from the proposed modified potential is studied. 相似文献
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Using the time-dependent pseudo-spectral scheme, we solve the time-dependent Schr ¨odinger equation of a hydrogenlike atom in a strong laser field in momentum space. The intensity-resolved photoelectron energy spectrum in abovethreshold ionization is obtained and further analyzed. We find that with the increase of the laser intensity, the abovethreshold ionization emission spectrum exhibits periodic resonance structure. By analyzing the population of atomic bound states, we find that it is the multi-photon excitation of bound state that leads to the occurrence of this phenomenon, which is in fairly good agreement with the experimental results. 相似文献
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Generalized Pseudospectral Method for Solving the Time-Dependent Schrodinger Equation Involving the Coulomb Potential 下载免费PDF全文
We present an accurate and efficient generalized pseudospectral method for solving the time-dependent Schrodinger equation for atomic systems interacting with intense laser fields. In this method, the time propagation of the wave function is calculated using the well-known second-order split-operator method implemented by the numerically exact, fast transform between the grid and spectral representations. In the grid representation, the radial coordinate is discretized using the Coulomb wave discrete variable representation (CWDVR), and the angular dependence of the wave function is expanded in the Gauss-Legendre-Fourier grid. In the spectral representation, the wave function is expanded in terms of the eigenfunctions of the field-free zero-order Hamiltonian. Calculations on the high order harmonic generation and ionization dynamics of hydrogen atom in strong laser pulses are presented to demonstrate the accuracy and efficiency of the present method. This new algorithm will be found more computationally attractive than the close-coupled wave packet method using CWDVR and/or methods based on evenly spaced grids. 相似文献
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发展了一套高精度、高效率的伪谱方法,以非微扰的方式求解真实原子三维含时Schrodinger方程.该方法选用二阶劈裂算符作为时间演化算子,分别选择能谱表象和坐标表象作为含时波函数演化的两个表象.在坐标表象下波函数的径向部分使用库仑波函数离散变量表象来离散;角向波函数展开在两维的Gauss-Legendre-Fourier格点上.以H原子的光激发和光电离过程为例,进行了数值计算并和解析解进行了比对.结果表明二者符合很好.该方法很好地处理了库仑奇点问题.还计算了强激光辐照H原子的多光子电离过程,并和其他的数值方案进行了比较.结果表明,在计算收敛的前提下本方法计算效率更高.Abstract: We present an accurate and effective pseudospectral method for solving the three-dimensional time-dependent Schrodinger equation involving the Coulomb potential. In this method, the Hamiltonian is evaluated by exploiting the two representations of the wave function. One is a grid representation, in which the angular dependence of the wave function is expanded in a two-dimensional Gauss-Legendre-Fourier grid in the coordinate space of polar and azimuthal angles. The radial coordinate is discretized using a discrete variable representation constructed from the Coulomb wave function (CWDVR) . The other is a spectral representation, in which the wave function is expanded in a set of square integrable functions chosen as the eigenfunctions of a zero-order Hamiltonian. The time of propagation of the wave function is calculated using the well-known second-order split-operator method implemented through the transform between the grid and spectral representations. Calculations on the photo-absorption strength of hydrogen atom are presented to demonstrate the accuracy of present method in low energy limit by the time-dependent wave-packet propagation method. As another example, the present method is applied to multiphoton ionization of H atom. For a wide range of field parameters, ionization rates calculated using the present method are in excellent agreement with those from other accurate numerical calculations. The new algorithm will be found more efficient than the close coupled wave packet method using CWDVR and/or methods based on evenly spaced grids. 相似文献