{"title":"Quantum expectation values and Shannon entropy in diatomic molecular systems","authors":"Etido P. Inyang","doi":"10.1007/s10910-025-01738-5","DOIUrl":null,"url":null,"abstract":"<div><p>This study investigates the expectation values and Shannon entropy of selected diatomic molecules—HCl, CO, and LiH—within the framework of the Kratzer plus Generalized Morse Potential. The energy eigenvalues and wave functions are determined using the parametric Nikiforov–Uvarov approach, enabling a detailed analysis of key quantum mechanical properties, including kinetic energy, squared momentum, and inverse square distance expectation values. Furthermore, Shannon entropy is applied to examine wave function localization in both position and momentum spaces, emphasizing the impact of screening parameters on molecular behavior. The findings indicate that an increase in the rotational quantum number results in higher energy spectra and expectation values. The Shannon entropy analysis reinforces the uncertainty principle by demonstrating an inverse relationship between position and momentum entropy. These insights contribute to quantum information measures in molecular systems, with potential applications in spectroscopy, molecular modeling, and quantum chemistry.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"63 8","pages":"1732 - 1752"},"PeriodicalIF":2.0000,"publicationDate":"2025-06-04","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/s10910-025-01738-5","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
This study investigates the expectation values and Shannon entropy of selected diatomic molecules—HCl, CO, and LiH—within the framework of the Kratzer plus Generalized Morse Potential. The energy eigenvalues and wave functions are determined using the parametric Nikiforov–Uvarov approach, enabling a detailed analysis of key quantum mechanical properties, including kinetic energy, squared momentum, and inverse square distance expectation values. Furthermore, Shannon entropy is applied to examine wave function localization in both position and momentum spaces, emphasizing the impact of screening parameters on molecular behavior. The findings indicate that an increase in the rotational quantum number results in higher energy spectra and expectation values. The Shannon entropy analysis reinforces the uncertainty principle by demonstrating an inverse relationship between position and momentum entropy. These insights contribute to quantum information measures in molecular systems, with potential applications in spectroscopy, molecular modeling, and quantum chemistry.
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.
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