{"title":"用水簇描述的Schrödinger方程的解集","authors":"K. E. Plokhotnikov","doi":"10.3103/S1541308X23030081","DOIUrl":null,"url":null,"abstract":"<p>A procedure is discussed for obtaining various solutions to the Schrödinger equation by the Monte Carlo method. Water clusters, namely, the hexamer 6(H<sub>2</sub>O), dodecamer 12(H<sub>2</sub>O), and tetradecamer 14(H<sub>2</sub>O) are used as quantum systems to illustrate the procedure. Various solutions to the Schrödinger equation are derived from the algorithm earlier proposed by the author, which is based on the intersection of the finite-difference and Monte Carlo approaches and on the water-cluster-tested methods for spatially reducing scattering centers of particle nuclei and scattering centers of electrons of an arbitrary quantum system. Ultimately, it has become possible to construct an algorithm for generating an unlimited number of various spatial structures of scattering clouds of particle nuclei and electrons at a given dissociation energy of a quantum system.</p>","PeriodicalId":732,"journal":{"name":"Physics of Wave Phenomena","volume":"31 3","pages":"151 - 159"},"PeriodicalIF":1.1000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Set of Solutions to the Schrödinger Equation as Illustrated with the Description of Water Clusters\",\"authors\":\"K. E. Plokhotnikov\",\"doi\":\"10.3103/S1541308X23030081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A procedure is discussed for obtaining various solutions to the Schrödinger equation by the Monte Carlo method. Water clusters, namely, the hexamer 6(H<sub>2</sub>O), dodecamer 12(H<sub>2</sub>O), and tetradecamer 14(H<sub>2</sub>O) are used as quantum systems to illustrate the procedure. Various solutions to the Schrödinger equation are derived from the algorithm earlier proposed by the author, which is based on the intersection of the finite-difference and Monte Carlo approaches and on the water-cluster-tested methods for spatially reducing scattering centers of particle nuclei and scattering centers of electrons of an arbitrary quantum system. Ultimately, it has become possible to construct an algorithm for generating an unlimited number of various spatial structures of scattering clouds of particle nuclei and electrons at a given dissociation energy of a quantum system.</p>\",\"PeriodicalId\":732,\"journal\":{\"name\":\"Physics of Wave Phenomena\",\"volume\":\"31 3\",\"pages\":\"151 - 159\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physics of Wave Phenomena\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.3103/S1541308X23030081\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physics of Wave Phenomena","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.3103/S1541308X23030081","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
On the Set of Solutions to the Schrödinger Equation as Illustrated with the Description of Water Clusters
A procedure is discussed for obtaining various solutions to the Schrödinger equation by the Monte Carlo method. Water clusters, namely, the hexamer 6(H2O), dodecamer 12(H2O), and tetradecamer 14(H2O) are used as quantum systems to illustrate the procedure. Various solutions to the Schrödinger equation are derived from the algorithm earlier proposed by the author, which is based on the intersection of the finite-difference and Monte Carlo approaches and on the water-cluster-tested methods for spatially reducing scattering centers of particle nuclei and scattering centers of electrons of an arbitrary quantum system. Ultimately, it has become possible to construct an algorithm for generating an unlimited number of various spatial structures of scattering clouds of particle nuclei and electrons at a given dissociation energy of a quantum system.
期刊介绍：
Physics of Wave Phenomena publishes original contributions in general and nonlinear wave theory, original experimental results in optics, acoustics and radiophysics. The fields of physics represented in this journal include nonlinear optics, acoustics, and radiophysics; nonlinear effects of any nature including nonlinear dynamics and chaos; phase transitions including light- and sound-induced; laser physics; optical and other spectroscopies; new instruments, methods, and measurements of wave and oscillatory processes; remote sensing of waves in natural media; wave interactions in biophysics, econophysics and other cross-disciplinary areas.
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