1、華東師范大學(xué)碩士學(xué)位論文磁薛定諤算子特征函數(shù)的零點(diǎn)集姓名：郭繼瑞申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：潘興斌20100501ABSTRACTInthispaper，weinvestigatenodalsetsofgroundstateeigenfunctionsofmagneticSchrSdingeroperatorsactingonanonsimplyconnecteddomaininⅡPBHelfferetalhaveinve

2、stigatedthisproblemwithzeromagneticfield，undertheeaseinwhichthecirculationofthemagneticvectorpotentialliesinZ1／2(see【HelDInthispaper，weappliedthemethodsofHMatanoetal，whichtheyhaveusedwhenstudyingzerosofGinzburgLandauorde

3、rparameter(see【EMQ])，togetageneralcharacteristicofnodalsetsofgroundstateeigenfunctionsofmagneticSchrSdingeroperatorsactingOilanonsimplyconnecteddomaininR2Subsequentlyundertheconditionofzeromagneticfield，wegeneralizethete

4、chniqueofcoveringmanifold，whichhasbeenusedinfHel]，tothecaseofthatthecirculationofthemagneticvectorpotentialliesinQBasedonthis，weprovesomeoriginalconclusionsincludingthatthenodalsetconsistsofisolatedpointsonlyinsomecases，

5、andthecurveswhichbelongtothenodalsetcouldnotslittheregioninsomeothercasesMoreover，fromthesefacts，wecouldunderstandthatthepropertyofnodalsetsunderappropriateconditionswillcompletelydifferfromthosediscussedin[Hel]Keywords：