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QuantumMechanics Designedforatwo-semesteradvancedundergraduateorgraduate-levelcourse,thisdistinc- tiveandmoderntextbookprovidesstudentswiththephysicalintuitionandmathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. BeginningwithadetailedintroductiontoquantumstatesandDiracnotation,thebookthen developstheoverarchingtheoreticalframeworkofquantummechanics,beforeexplaining physicalquantum-mechanicalpropertiessuchasangularmomentumandspin.Symmetries andgroupsinquantummechanics,importantcomponentsofcurrentresearch,arecovered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerousexercisesareinterspersedthroughoutthetext,expandinguponkeyconceptsand further developing students’understanding. Afullyworked solutions manualand lecture slidesareavailableforinstructors. ArjunBerera is Professor in Physics at the University of Edinburgh. He has held research positions in the USA before joining the faculty at Edinburgh. His research is focused on quantumfieldtheoryandstatisticalphysicsandhehaspublishedextensivelyintheseareas. Hehasovertwodecadesofteachingexperienceatbothundergraduateandgraduatelevel acrossarangeofcourses,includingquantummechanicsandstatisticalmechanics. LuigiDelDebbioisProfessorinPhysicsattheUniversityofEdinburgh.Hehasheldresearch positions in the UK, France, Italy and at CERN, before joining the faculty at Edinburgh. Hisresearchiscentredonnon-perturbativeaspectsoffieldtheoriesandtheirapplicationto particlephysics.Hehasextensiveteachingexperienceatbothundergraduateandgraduate level and has been the Programme Coordinator for the Mathematical Physics degree at Edinburghforanumberofyears. ‘Berera and Del Debbio do a wonderful job of walking the reader through the mathematics of quantumtheory,nevershyingawayfromthenecessarycomplexitieswhilekeepingthingsassimple astheycanbe.’ DavidTong,UniversityofCambridge ‘Today’squantummechanicsstudentsshouldlearnnotonlytheharmonicoscillatorandthehydrogen atom,butalsoentanglementandquantuminformation.Thisbooktreatstheoldandthenewwithgreat clarity,includingafirstlookatquantumcomputationthroughtheDeutschandGroveralgorithms. Anotherhighlightisthecollectionofwell-craftedproblems.’ MatthewReece,HarvardUniversity ‘This text promises to be useful to a wide audience, from intermediate-level undergraduates to beginning graduate students. It is pedagogical and rather complete, and attempts to guide readers with different backgrounds via gentle yet precise mathematical asides. The chapter on quantumentanglementisthemostcomprehensiveandcompletediscussionofthetopicinabroad quantum mechanics textbook and will play an important role in introducing twenty-first-century undergraduatestothecontemporaryandrapidlygrowingfieldofquantumcomputing.’ Andre´deGouveâ,NorthwesternUniversity ‘Quantummechanicsisdifficulttoteachasitdefiesintuitionsofeverydayexperience.Thetextbook byBereraandDelDebbiogroundsthesubjectbylayingitsmathematicalfoundationsfirst,giving studentsacoherentframeworkdistilledfromacenturyofteachingexperience.Filledwithhelpful exercisesandmoderntopicsincludingquantuminformationtheory,thisbookwouldbeanexcellent textforbothundergraduateandgraduatecourses.’ MaximLavrentovich,UniversityofTennessee,Knoxville ‘Oneofthebestfeaturesofthisbookisthesubstantialchapteronquantumentanglement,quantum computing and information theory (Bell’s inequality, no-cloning theorem, quantum teleportation). It is based on early introduction of the mathematical foundations and Dirac notation. Beyond the standard topics, students will appreciate the inclusion of symmetry groups, applications involving multi-electronsystems,theWKB(J)method,thediscussionoftheDiracequation,andanin-depth treatmentofquantumscattering.’ RussellHerman,UniversityofNorthCarolina ‘Aconciseyetcompleteintroductiontoquantummechanicsattheundergraduatelevel.Theauthors doagreatjobofexploringtheformalandqualitativeaspectsofthetheory,aswellasmoremodern topicsofinterestsuchasquantumcomputation.’ ChristopherAubin,FordhamUniversity ‘Arjun Berera and Luigi Del Debbio’s Quantum Mechanics is an exceptional textbook. It, of course, offers superb coverage of the requisite material for a standard two-semester upper-level undergraduatequantummechanics(QM)course.Nonetheless,thetextbookismuchricherthanthat. Twofeaturesmakeitunique:Chapter1,“StoriesandThoughtsaboutQuantumMechanics”,presents adetailedandlivelyhistoryof“thetortuouspaththatledtotheformationofthetheoryasweknow it”.Thisreadingbothisentertainingandsetsthegroundworkforthechaptersthatfollow.Alsoof specialnoteisChapter15,“QuantumEntanglement”.Whilequantumentanglementhaslongraised theoretical questions regarding freedom and the nature of reality, within the last two decades its applicationshaveburstforthnotjustinphysics,butalsoinengineering,computing,encryptionand communications. Through very informative chapter readings and well-chosen problems, students willmasterassociatedkeyconcepts,suchascalculatingandinterpretingBell’sinequality;informa- tiontheoryandShannonandvonNeumannentropies;theno-cloningtheorem,quantumteleportation and superdense coding; and quantum register and logic gates, Deutsch’s algorithm and Grover’s algorithm.Thistextbooksetsthestandardforquantumentanglementcoverage.Iardentlypromote ArjunBereraandLuigiDelDebbio’sQuantumMechanics.’ GeraldB.Cleaver,BaylorUniversity ‘Lucid introduction to a complex subject accessible to advanced undergraduate and beginning graduatestudentsinscienceandengineering.Theauthorscombinephysicalinsightandmathematical rigourinexplainingabstractconceptswithavarietyofexamples.Coversallthequintessentialtopics inthefield,aswellasavaluablemodernintroductiontoquantumentanglement.’ KaladiBabu,OklahomaStateUniversity Quantum Mechanics ARJUN BERERA UniversityofEdinburgh LUIGI DEL DEBBIO UniversityofEdinburgh UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom OneLibertyPlaza,20thFloor,NewYork,NY10006,USA 477WilliamstownRoad,PortMelbourne,VIC3207,Australia 314–321,3rdFloor,Plot3,SplendorForum,JasolaDistrictCentre,NewDelhi–110025,India 103PenangRoad,#05–06/07,VisioncrestCommercial,Singapore238467 CambridgeUniversityPressispartoftheUniversityofCambridge. ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof education,learning,andresearchatthehighestinternationallevelsofexcellence. www.cambridge.org Informationonthistitle:www.cambridge.org/9781108423335 DOI:10.1017/9781108525848 ©ArjunBereraandLuigiDelDebbio2022 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2022 PrintedintheUnitedKingdombyTJBooksLimited,Padstow,Cornwall AcataloguerecordforthispublicationisavailablefromtheBritishLibrary. LibraryofCongressCataloging-in-PublicationData Names:Berera,Arjun,1964-author. Title:Quantummechanics/ArjunBerera,LuigiDelDebbio. Description:NewYork:CambridgeUniversityPress,2021.|Includes bibliographicalreferencesandindex. Identifiers:LCCN2021024878(print)|LCCN2021024879(ebook)| ISBN9781108423335(hardback)|ISBN9781108525848(epub) Subjects:LCSH:Quantumtheory.|BISAC:SCIENCE/Physics/QuantumTheory Classification:LCCQC174.12.B45552021(print)|LCCQC174.12(ebook)| DDC530.12–dc23 LCrecordavailableathttps://lccn.loc.gov/2021024878 LCebookrecordavailableathttps://lccn.loc.gov/2021024879 ISBN978-1-108-42333-5Hardback Additionalresourcesforthispublicationatwww.cambridge.org/bereradeldebbio CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain, accurateorappropriate. Forourparents