Linearity, Symmetry, and Prediction in the Hydrogen Atom

Thepredictivepowerofmathematicsinquantumphenomenaisoneofthegreatintellectualsuccessesofthe20thcentury.Thistextbook,aimedatundergraduateorgraduatelevelstudents(dependingonthecollegeoruniversity),concentratesonhowtomakepredictionsaboutthenumbersofeachkindofbasicstateofaquantumsystemfromonlytwoingredients:thesymmetryandthelinearmodelofquantummechanics.Thismethod,involvingthemathematicalareaofrepresentationtheoryorgrouptheory,combinesthreecoremathematicalsubjects,namely,linearalgebra,analysisandabstractalgebra.Wideapplicationsofthismethodoccurincrystallography,atomicstructure,classificationofmanifoldswithsymmetry,andotherareas.Thetopicsunfoldsystematically,introducingthereaderfirsttoanimportantexampleofaquantumsystemwithsymmetry,thesingleelectroninahydrogenatom.Thenthereaderisgivenjustenoughmathematicaltoolstomakepredictionsaboutthenumbersofeachkindofelectronicorbitalbasedsolelyonthephysicalsphericalsymmetryofthehydrogenatom.Thefinalchaptersaddresstherelatedideasofquantumspin,measurementandentanglement.Thisuser-friendlyexposition,drivenbynumerousexamplesandexercises,requiresasolidbackgroundincalculusandfamiliaritywitheitherlinearalgebraoradvancedquantummechanics.Linearity,Symmetry,andPredictionintheHydrogenAtomwillbenefitstudentsinmathematics,physicsandchemistry,aswellasaliterategeneralreadership.Aseparatesolutionsmanualisavailabletoinstructors.