Schrödinger-Poisson系统解的存在性-豆柴文库

您所在位置：网站首页 / Schrödinger-Poisson系统解的存在性.docx / 文档详情

在线预览结束，喜欢就下载吧，查找使用更方便

5 金币

下载文档

/ 2

下载提示

如果您无法下载资料，请参考说明：

1、部分资料下载需要金币，请确保您的账户上有足够的金币

2、已购买过的文档，再次下载不重复扣费

3、资料包下载后请先用软件解压，在使用对应软件打开

文本预览

Schrödinger-Poisson系统解的存在性
Title:TheExistenceofSolutionsintheSchrödinger-PoissonSystem
Abstract:
Inthispaper,wediscusstheexistenceofsolutionsintheSchrödinger-Poissonsystem.TheSchrödinger-Poissonsystemisafundamentalmodelinquantummechanicsthatdescribestheinteractionbetweenparticlessubjecttoapotentialfield.Wereviewthetheoreticalfoundationsofthesystem,analyzethepropertiesoftheequations,andpresentthemostrecentdevelopmentsinthefield.Byemployingvariousmathematicaltools,wedemonstratetheexistenceofsolutionsandexplorethephysicalimplicationsofthesesolutions.
1.Introduction
TheSchrödinger-PoissonsystemisacoupledsystemofequationsthatcombinestheSchrödingerequation,describingthewavefunctionofquantumparticles,withthePoissonequation,describingthegravitationalpotential.Thissystemarisesinvariousphysicalphenomena,suchassemiconductorphysics,plasmaphysics,andastrophysics.Themaingoalofthispaperistoestablishtheexistenceofsolutionstothissystem.
2.TheoreticalFoundations
WebeginbydiscussingthemathematicalformulationoftheSchrödinger-Poissonsystem.WeintroducetheSchrödingerequationandthePoissonequation,outliningtheirphysicalinterpretationsandmathematicalproperties.ThecouplingbetweentheseequationsarisesfromthepotentialtermintheSchrödingerequation,whichisdeterminedbythegravitationalpotentialdescribedbythePoissonequation.
3.AnalyzingtheEquations
WeanalyzetheequationsoftheSchrödinger-Poissonsystemtounderstandtheirbehaviorandproperties.Wediscussthewell-posednessoftheequations,theircompatibilityconditions,andpossibleconstraintsonthesolutions.Byexaminingthenonlinearnatureofthesystem,wehighlightthechallengesinestablishingtheexistenceofsolutions.
4.MathematicalTools
ToaddressthenonlinearandcouplednatureoftheSchrödinger-Poissonsystem,weemployvariousmathematicaltechniques.Weexploretheuseofthefixed-pointtheorem,variationalmethods,andlinearizationapproaches.Additionally,wediscussthesignificanceofSobolevspacesandtheirroleinestablishingexistenceresultsforthesystem.
5.ExistenceofSolutions
Wepresentthemainresult