Improved rotating Kratzer–Fues oscillator: eigenenergies, eigenfunctions, coherent states and ladder operators

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-03-16 DOI:10.1007/s10910-024-01585-w

Marcin Molski

{"title":"Improved rotating Kratzer–Fues oscillator: eigenenergies, eigenfunctions, coherent states and ladder operators","authors":"Marcin Molski","doi":"10.1007/s10910-024-01585-w","DOIUrl":null,"url":null,"abstract":"<div>Exact analytical energy formula for the rotating Kratzer–Fues oscillator with (v, J)-dependent potential parameters is obtained. It was used to reproduce the spectral data generated by the vibrational transitions \\(v\\rightarrow v+1, v=0, 1 \\ldots 7\\) in \\(J=0,1\\ldots 47\\) rotational states of dinitrogen \\(^{14}\\)N\\(_2\\) and \\(^{15}\\)N\\(_2\\) in the ground electronic state \\(X^1\\Sigma _g^+\\). Calculations performed for two isotopic variants enabled the selection of the mass-dependent and independent potential parameters defining the model. To check the ability of the eigenenergies derived to reproduce rotational transitions measured with kHz accuracy, calculations for \\(^{74}\\)Ge\\(^{32}\\)S, \\(^{79}\\)Br\\(^{35}\\)Cl and \\(^{1}\\)H\\(^{35}\\)Cl were performed, obtaining agreement between theoretical and experimental results. Minimum uncertainty coherent states and ladder operators for the rotating improved Kratzer–Fues oscillator are also constructed.</div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":null,"pages":null},"PeriodicalIF":1.7000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-024-01585-w","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 0

Abstract

Exact analytical energy formula for the rotating Kratzer–Fues oscillator with (v, J)-dependent potential parameters is obtained. It was used to reproduce the spectral data generated by the vibrational transitions \(v\rightarrow v+1, v=0, 1 \ldots 7\) in \(J=0,1\ldots 47\) rotational states of dinitrogen \(^{14}\)N\(_2\) and \(^{15}\)N\(_2\) in the ground electronic state \(X^1\Sigma _g^+\). Calculations performed for two isotopic variants enabled the selection of the mass-dependent and independent potential parameters defining the model. To check the ability of the eigenenergies derived to reproduce rotational transitions measured with kHz accuracy, calculations for \(^{74}\)Ge\(^{32}\)S, \(^{79}\)Br\(^{35}\)Cl and \(^{1}\)H\(^{35}\)Cl were performed, obtaining agreement between theoretical and experimental results. Minimum uncertainty coherent states and ladder operators for the rotating improved Kratzer–Fues oscillator are also constructed.

查看原文本刊更多论文

改进的旋转克拉策-福斯振荡器：特征能、特征函数、相干态和梯形算子

获得了具有（v, J）相关势参数的旋转克拉策-富斯振荡器的精确分析能量公式。它被用于重现二氮旋转态（J=0,1\ldots 47\）中的振动跃迁（v\rightarrow v+1, v=0, 1 \ldots 7\）和基态电子态（X^1\Sigma _g^+\）中的振动跃迁（(^{14}\)N\(_2\)和(^{15}\)N\(_2\)）所产生的光谱数据。通过对两种同位素变体的计算，可以选择定义模型的与质量相关的独立电势参数。为了检验推导出的特征能重现以千赫精度测量的旋转转变的能力，对 \(^{74}\)Ge\(^{32}\)S, \(^{79})Br\(^{35}\)Cl 和 \(^{1}\)H\(^{35}\)Cl 进行了计算，在理论和实验结果之间取得了一致。此外，还构建了旋转改进克拉策-富斯振荡器的最小不确定性相干态和梯算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.