Numerical-Methods-in-Quantum-Mechanics

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1、LecturenotesNumericalMethodsinQuantumMechanicsCorsodiLaureaMagistraleinFisicaInterateneoTrieste{UdineAnnoaccademico2012/2013PaoloGiannozziUniversityofUdineContainssoftwareandmaterialwrittenbyFurioErcolessi1andStefanodeGironcoli21FormerlyatUniversityofUdine2SISSA-Trieste

2、LastmodiedMay23,2013ContentsIntroduction10.1AboutSoftware............................10.1.1Compilers...........................10.1.2VisualizationTools......................20.1.3MathematicalLibraries...................20.1.4PitfallsinC-Fortraninterlanguagecalls.......

3、...30.2Bibliography.............................41One-dimensionalSchr•odingerequation51.1Theharmonicoscillator.......................51.1.1Units.............................61.1.2Exactsolution........................61.1.3Comparisonwithclassicalprobabilitydensity.......

4、81.2Quantummechanicsandnumericalcodes:someobservations..91.2.1Quantization.........................91.2.2Apitfall:pathologicalasymptoticbehavior........91.3Numerov'smethod..........................101.3.1Code:harmonic0.......................121.3.2Code:harmonic1........

5、...............131.3.3Laboratory..........................152Schr•odingerequationforcentralpotentials162.1Variableseparation..........................162.1.1Radialequation........................182.2Coulombpotential..........................182.2.1Energylevels.........

6、................202.2.2Radialwavefunctions....................202.3Code:hydrogenradial........................212.3.1Logarithmicgrid.......................212.3.2Improvingconvergencewithperturbationtheory.....222.3.3Laboratory..........................243Scatteringfroma

7、potential253.1Shortreminderofthetheoryofscattering.............253.2ScatteringofHatomsfromraregases...............273.2.1DerivationofVanderWaalsinteraction..........27i3.3Code:crossection...........................283.3.1Laboratory..........................304TheVariati

8、onalMethod324.1VariationalPrinciple.........................324.1.1Demonstrationofthevariationalprinciple.....