{"title":"谐波固体","authors":"R. Swendsen","doi":"10.1093/ACPROF:OSO/9780199646944.003.0025","DOIUrl":null,"url":null,"abstract":"In Chapter 26 we return to calculating the contributions to the specific heat of a crystal from the vibrations of the atoms. The vibrations of a model of a solid, for which the interactions are quadratic in form, is investigated. Calculations are restricted to one dimension for simplicity in the derivations of the Fourier modes and the equations of motion. Both pinned and periodic boundary conditions are discussed. The representation of the Hamiltonian in terms of normal modes and the solution in terms of the equations of motion are derived. The Debye approximation is then introduced for three-dimensional systems.","PeriodicalId":102491,"journal":{"name":"An Introduction to Statistical Mechanics and Thermodynamics","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Harmonic Solid\",\"authors\":\"R. Swendsen\",\"doi\":\"10.1093/ACPROF:OSO/9780199646944.003.0025\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In Chapter 26 we return to calculating the contributions to the specific heat of a crystal from the vibrations of the atoms. The vibrations of a model of a solid, for which the interactions are quadratic in form, is investigated. Calculations are restricted to one dimension for simplicity in the derivations of the Fourier modes and the equations of motion. Both pinned and periodic boundary conditions are discussed. The representation of the Hamiltonian in terms of normal modes and the solution in terms of the equations of motion are derived. The Debye approximation is then introduced for three-dimensional systems.\",\"PeriodicalId\":102491,\"journal\":{\"name\":\"An Introduction to Statistical Mechanics and Thermodynamics\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"An Introduction to Statistical Mechanics and Thermodynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0025\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"An Introduction to Statistical Mechanics and Thermodynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/ACPROF:OSO/9780199646944.003.0025","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In Chapter 26 we return to calculating the contributions to the specific heat of a crystal from the vibrations of the atoms. The vibrations of a model of a solid, for which the interactions are quadratic in form, is investigated. Calculations are restricted to one dimension for simplicity in the derivations of the Fourier modes and the equations of motion. Both pinned and periodic boundary conditions are discussed. The representation of the Hamiltonian in terms of normal modes and the solution in terms of the equations of motion are derived. The Debye approximation is then introduced for three-dimensional systems.
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