Quantum Theory for Mathematicians (Graduate Texts in Mathematics)

Althoughideasfromquantumphysicsplayanimportantroleinmanypartsofmodernmathematics,therearefewbooksaboutquantummechanicsaimedatmathematicians.Thisbookintroducesthemainideasofquantummechanicsinlanguagefamiliartomathematicians.Readerswithlittlepriorexposuretophysicswillenjoythebook'sconversationaltoneastheydelveintosuchtopicsastheHilbertspaceapproachtoquantumtheory;theSchrödingerequationinonespacedimension;theSpectralTheoremforboundedandunboundedself-adjointoperators;theStone–vonNeumannTheorem;theWentzel–Kramers–Brillouinapproximation;theroleofLiegroupsandLiealgebrasinquantummechanics;andthepath-integralapproachtoquantummechanics.Thenumerousexercisesattheendofeachchaptermakethebooksuitableforbothgraduatecoursesandindependentstudy.Mostofthetextisaccessibletograduatestudentsinmathematicswhohavehadafirstcourseinrealanalysis,coveringthebasicsofL2spacesandHilbertspaces.Thefinalchaptersintroducereaderswhoarefamiliarwiththetheoryofmanifoldstomoreadvancedtopics,includinggeometricquantization.