Solving the time-dependent Schroedinger equation by discarding high-energy basis functions

McLeod M.; Carrington Jr. T.

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Solving the time-dependent Schroedinger equation by discarding high-energy basis functions

机译：通过抛弃高能基函数来求解时间相关的Schroedinger方程

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It is demonstrated that it is possible to solve the time-dependent Schroedinger equation in 10d by discarding unimportant product basis functions. The matrix-vector products required to propagate an initial wave packet are done at a cost that scales as nD+1 where n is a representative number of 1D basis functions and D is the dimensionality. Discarding unimportant basis functions drastically reduces the size of the vectors that must be stored. With D=20 and n=16 only ～26 GB is required to store the wavefunction. The ideas are applied to a model Hamiltonian for hydrocarbon chains.

机译：结果表明，通过抛弃不重要的乘积基函数，可以在10d内求解与时间相关的Schroedinger方程。传播初始波包所需的矩阵向量乘积以nD + 1的代价完成，其中n是一维基函数的代表数，D是维数。舍弃不重要的基函数会极大地减少必须存储的向量的大小。在D = 20和n = 16的情况下，仅需要约26 GB的存储波函数。这些想法被应用于碳氢化合物链的哈密顿模型。

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《Chemical Physics Letters》 |2010年第3期|共4页
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McLeod M.; Carrington Jr. T.;
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1. Solving the time-dependent Schroedinger equation by discarding high-energy basis functions [J] . McLeod M., Carrington Jr. T. Chemical Physics Letters . 2010,第1a3期

机译：通过抛弃高能基函数来求解时间相关的Schroedinger方程
2. A local radial basis function-finite difference (RBF-FD) method for solving 1D and 2D coupled Schroedinger-Boussinesq (SBq) equations [J] . OEmer Oruc Engineering analysis with boundary elements . 2021,第Auga期

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3. TOWARDS NUMERICALLY SOLVING THE TWO-DIMENSIONAL TIME-DEPENDENT SCHROEDINGER EQUATION FOR LONG-LIVED DECAYING STATES [J] . NICOLAE CARJAN, DAN STROTTMAN, MARGARIT RIZEA Romanian journal of physics . 2002,第1a2期

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4. Symbolic-Numerical Algorithm for Solving the Time-Dependent Schroedinger Equation by Split-Operator Method [C] . Alexander Gusev, Vladimir Gerdt, Michail Kaschiev, International Workshop on Computer Algebra in Scientific Computing(CASC 2005); 20050912-16; Kalamata(GR) . 2005

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6. Communication: An exact short-time solver for the time-dependent Schrödinger equation [O] . Zhigang Sun, Weitao Yang -1

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Solving the time-dependent Schroedinger equation by discarding high-energy basis functions

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