SOLUTION OF THE SCHRODINGER-EQUATION BY A SPECTRAL METHOD
SOLUTION OF THE SCHRODINGER-EQUATION BY A SPECTRAL METHOD
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DOI：
10.1016/0021-9991(82)90091-2
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发表时间：
1982-01-01
影响因子：
4.1
通讯作者：
STEIGER, A
中科院分区：
文献类型：
--
作者：
FEIT, MD;FLECK, JA;STEIGER, A
描述了确定Schrödinger方程特征值和特征函数的一种新的计算方法。解决这一问题的传统方法依赖于哈密顿矩阵的对角化或时间无关波动方程的迭代数值解。相比之下，新方法是基于时变薛定谔方程解的谱性质。该方法要求从一个数值解ψ(r,t)中计算一个相关函数<ψ(r, 0)| ψ(r,t)>。该相关函数的傅里叶分析揭示了一组对应于系统稳态的共振峰。对这些峰的位置进行分析，得到了精度较高的特征值。ψ(r,t)关于时间的附加傅里叶变换产生了特征函数。对于一维非对称双井势和二维hsamnon - heiles势，证明了该方法的有效性。
A new computational method for determining the eigenvalues and eigenfunctions of the Schrödinger equation is described. Conventional methods for solving this problem rely on diagonalization of a Hamiltonian matrix or iterative numerical solutions of a time independent wave equation. The new method, in contrast, is based on the spectral properties of solutions to the time-dependent Schrodinger equation. The method requires the computation of a correlation function <ψ(r, 0)| ψ(r,t)> from a numerical solution ψ(r,t). Fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system. Analysis of the location of these peaks reveals the eigenvalues with high accuracy. Additional Fourier transforms of ψ(r,t) with respect to time generate the eigenfunctions. The effectiveness of the method is demonstrated for a one-dimensional asymmetric double well potential and for the two-dimensional Hénon-Heiles potential.