Discrete variable representations of complicated kinetic energy operators
Discrete variable representations of complicated kinetic energy operators
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复杂动能算子的离散变量表示
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
T. Carrington
中科院分区：
文献类型：
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作者：
Huazhou Wei;T. Carrington
离散变量表示（DVR）最重要的优点可能是它的简单性。DVR势能矩阵直接由势函数构造，不需要求积分。对于简单动能算子，DVR动能矩阵由原始离域多项式基集中一维动能算子的变换矩阵和精确矩阵表示确定。对于复杂的动能算子，其项或因子的导数的矩阵元素必须通过数值计算，定义一个DVR是比较困难的。DVR可以从有限基表示（FBR）中定义，其中动能算子中项或因子的矩阵元素通过正交计算，但隐含的正交破坏了DVR的简单性和便利性。可以通过用矩阵表示的乘积代替每个动能算子项的矩阵表示来绕过正交。本产品适用于…
Probably the most important advantage of the discrete variable representation (DVR) is its simplicity. The DVR potential energy matrix is constructed directly from the potential function without evaluating integrals. For simple kinetic energy operators the DVR kinetic energy matrix is determined from transformation matrices and exact matrix representations of one‐dimensional kinetic energy operators in the original delocalized polynomial basis set. For complicated kinetic energy operators, for which matrix elements of terms or factors with derivatives must be calculated numerically, defining a DVR is harder. A DVR may be defined from a finite basis representation (FBR) where matrix elements of terms or factors in the kinetic energy operator are computed by quadrature but implicating quadrature undermines the simplicity and convenience of the DVR. One may bypass quadrature by replacing the matrix representation of each kinetic energy operator term with a product of matrix representations. This product appr...