INTERMEDIATE HAMILTONIANS AS A NEW CLASS OF EFFECTIVE-HAMILTONIANS
INTERMEDIATE HAMILTONIANS AS A NEW CLASS OF EFFECTIVE-HAMILTONIANS
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DOI：
10.1088/0305-4470/18/5/014
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发表时间：
1985-01-01
期刊：
影响因子：
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通讯作者：
DAUDEY, JP
中科院分区：
文献类型：
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作者：
MALRIEU, JP;DURAND, P;DAUDEY, JP
有效哈密顿理论已经建立起来了。然而，它在处理分子物理和量子化学中的许多问题时表现出了局限性。当定义标准有效哈密顿量的模型空间和外层空间之间存在大的耦合时，标准有效哈密顿量可能变成强非厄米的。此外，在存在入侵态的情况下，这些有效哈密顿量的矩阵元素作为核间距离的函数出现不连续。为了解决这些困难，提出了一类新的有效哈密顿量(称为中间哈密顿量)；它们的根只有一部分是完全哈密顿量的精确本征能量。这些中间哈密顿量的理论是借助于一种新的波算符R提出的，它类似于有效哈密顿理论中的波算符Omega。解由广义简并摄动理论(GDPT)和迭代程序得到。数值求解了两个模型系统，证明了GDPT相对于标准简并摄动理论(DPT)具有良好的收敛特性。在存在入侵者状态的情况下，还检查了解的连续性。
The theory of effective Hamiltonians is well established. However, limitations appear in its applicability for many problems in molecular physics and quantum chemistry. The standard effective Hamiltonians may become strongly non-Hermitian when there is a large coupling between the model space, in which they are defined, and the outer space Moreover, in the presence of intruder states, discontinuities appear in the matrix elements of these effective Hamiltonians as a function of the internuclear distances. To solve these difficulties, a new class of effective Hamiltonians (called intermediate Hamiltonians) is presented; only one part of their roots are exact eigen-energies of the full Hamiltonian. The theory of these intermediate Hamiltonians is presented by means of a new wave-operator R which is the analogue of the wave-operator Omega in the theory of effective Hamiltonians. Solutions are obtained by a generalised degenerate perturbation theory (GDPT) and by iterative procedures. Two model systems are numerically solved which demonstrate the good convergence properties of GDPT with respect to standard degenerate perturbation theory (DPT). Continuity of the solutions is also checked in the presence of an intruder state.