莫尔斯振子的阶梯算子及摄动振动问题

IF 2.5 2区 化学 Q3 CHEMISTRY, PHYSICAL International Reviews in Physical Chemistry Pub Date : 2019-01-02 DOI:10.1080/0144235X.2019.1593583
S. V. Krasnoshchekov, Xuanhao Chang
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引用次数: 5

摘要

求解多原子振动Schrödinger方程的量子力学方法需要比源自谐振子(HO)的方法更高质量的零阶近似。建立在HO上的阶梯算子具有许多独特的特征,简化了算子摄动理论和基于矩阵元素的方法的实际实现。因此,为可解非调和振子,主要是莫尔斯振子寻找合适的阶梯算子仍然是核振动动力学的主要挑战之一。在这项工作中,我们回顾了摩尔斯振荡器阶梯算子(MLOs)的建立问题,并展望了它们在解决多维非谐波振动问题的各种方法中的应用。探讨和分析了几种现有的mlo构建方法的特点。因式分解法得到的原生MLOs不太适合表示扰动势能算子。超对称量子力学(SUSYQM)也不能解决这个问题,因为相应的阶梯算符只是连接相关势的状态。SU(2)振子模型提供了基于能态形式同构的近似解。我们发现目前唯一有用的MLOs模型是基于所谓的拟数态基集(QNSB),它建立在修正的拉盖尔多项式上。QNSB给出了精确解对应的莫尔斯哈密顿量的有限三对角矩阵表示。以HF分子为例说明了QNSB方法与二阶/四阶微扰理论相比的方便性和准确性。总的结论是,基于qnsb的MLOs适用于构建多体治疗,例如,使用VSCF/VCI方法。
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Ladder operators for Morse oscillator and a perturbed vibrational problem
ABSTRACT Quantum-mechanical methods of solving the polyatomic vibrational Schrödinger equation need higher quality zero-order approximations than ones originating from the harmonic oscillator (HO). Ladder operators built on the HO have a number of unique features simplifying both the operator perturbation theory and practical implementations of matrix-elements-based methods. Therefore, finding suitable ladder operators for solvable anharmonic oscillators and mainly the Morse oscillator remain one of the major challenges of nuclear vibrational dynamics. In this work, we review the problem of building Morse oscillator ladder operators (MLOs) and the prospects of their use in various methods of solving the many-dimensional anharmonic vibrational problem. The features of several existing approaches for building MLOs are explored and analysed. The native MLOs obtained by the factorisation method are not quite suitable for expressing a perturbed potential energy operator. Supersymmetric quantum mechanics (SUSYQM) does not solve the problem either since corresponding ladder operators only connect states from related potentials. The SU(2) vibron model provides an approximate solution based on a formal isomorphism of energy states. We have found that for the present the only useful model for MLOs is based on the so-called quasi-number states basis set (QNSB) built on modified Laguerre polynomials. QNSB yields a finite tridiagonal matrix representation of the Morse Hamiltonian corresponding to the exact solution. The convenience and accuracy of QNSB approach in comparison to second/fourth-order perturbation theory is illustrated with the HF molecule. The general conclusion is that QNSB-based MLOs are suitable for building many-body treatments, for instance, with the VSCF/VCI approach.
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来源期刊
CiteScore
14.20
自引率
1.60%
发文量
5
审稿时长
1 months
期刊介绍: International Reviews in Physical Chemistry publishes review articles describing frontier research areas in physical chemistry. Internationally renowned scientists describe their own research in the wider context of the field. The articles are of interest not only to specialists but also to those wishing to read general and authoritative accounts of recent developments in physical chemistry, chemical physics and theoretical chemistry. The journal appeals to research workers, lecturers and research students alike.
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