Table Of ContentOUPCORRECTEDPROOF – FINAL,10/3/2020,SPi
Quantum Mechanics for Beginners
OUPCORRECTEDPROOF – FINAL,10/3/2020,SPi
OUPCORRECTEDPROOF – FINAL,10/3/2020,SPi
Quantum
Mechanics
for Beginners
with applications to quantum
communication and
quantum computing
M. Suhail Zubairy
TexasA&MUniversity
1
OUPCORRECTEDPROOF – FINAL,10/3/2020,SPi
3
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ISBN978–0–19–885422–7(hbk.)
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Preface
The laws of quantum mechanics were formulated about a hundred years ago, replacing the
classical laws of Newton and Maxwell. Since then, quantum mechanics has been applied
remarkably successfully to understand a very wide range of observations and systems. The
success of the laws of quantum mechanics in predicting and explaining essentially all the
knownphysicalphenomenaisastounding.However,inspiteofthegreatsuccess,itremains
a mysterious theory and the concepts of wave–particle duality, complementarity, the prob-
abilistic nature of measurement, quantum interference, and quantum entanglement are still
hotly discussed. However, it is not just the remarkable success in explaining all the known
phenomenathatmakesquantummechanicsafascinatingsubject.Itistrulyamazingthat,even
today,amereknowledgeofthebasicpostulatescanleadtostartlingnewideasanddevices.For
example,justtheknowledgeoftheprincipleofcomplementaritycanleadtoperfectlysecure
communicationsystems,ortheunderstandingofabeamsplitterforasinglephotoncanleadto
ahighlycounterintuitivecommunicationprotocolwithnoparticlepresentinthetransmission
channel, or the resource of quantum entanglement can lead to novel quantum computing
algorithms. Therefore it becomes possible to convey not only the foundations of quantum
mechanics but also some mind-boggling applications, such as in quantum communication
andquantumcomputing,withjustelementaryknowledgeofbasicphysicsandmathematics.
With this background it is interesting to ask whether it is possible to convey the basic
concepts of quantum mechanics and its amazing applications to someone with a limited
knowledge of physics and mathematics. In the fall of 2018, I offered a course on Quantum
MechanicstoincomingfreshmanstudentsatTexasA&MUniversity.Thesestudents,justoutof
highschool,tookthiscoursebeforetheytooktheusualMechanicsandElectricity/Magnetism
courses.Thisbookgrewoutofthelecturenotesofthiscourse.Themainobjectiveofthisbookis
topresentanintroductiontoquantummechanicsinanalmostself-containedwayforsomeone
withahighschoolphysicsandmathematicsbackground.
The book challenges the common perception that quantum mechanics is a highly math-
ematicalandabstract subject thatisinaccessibletoanyonewithoutanadvanced knowledge
of mathematics. This book, except the last chapter on the Schrödinger equation, is entirely
algebra-based.Aneffortismadetoderivesomeamazingresultsfromverysimpleideasandele-
mentarymathematicaltools.Ideallyeverychapteroffersresultsthatarehighlycounterintuitive
andinteresting.Thisbookcanbeusedasatextforacourseonquantummechanicsorquantum
informaticsattheundergraduatelevel.Howeveritcanalsobeausefulandaccessiblebookfor
thosewhoarenotfamiliarwithbutwanttolearnsomeofthefascinatingrecentandongoing
developmentsinareasrelatedtothefoundationofquantummechanicsanditsapplicationsto
areassuchasquantumcommunicationandquantumcomputing.
Thebookisdividedintofourparts.Afteranintroductorychapter,somebasicmathematical
toolssuchas complexnumbers,vectoranalysis,andintroductiontoprobability aswell asa
classicaldescriptionofparticles and wavesareintroduced in thenextthreechapters. Inthe
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viii PREFACE
nexteightchapters,basicconceptsofquantummechanicsarediscussed,suchaswave–particle
duality, complementarity, the Heisenberg uncertainty relation, quantum interference and
entanglement,no-cloningtheorem,aswellasissuesatthefoundationsofquantummechanics
suchasthedelayed-choicequantumeraser,theSchrödinger’scatandEPRparadoxes,andBell
theorem. In the following chapters, these fundamentals of quantum mechanics are applied
to applications in areas such as secure quantum communication, quantum teleportation,
counterfactualcommunication,andquantumcomputation.Inthelastpart,theSchrödinger
equation is introduced with its relation to Newtonian dynamics and its applications for a
particleinsideaboxandthehydrogenatom.
Each chapter is followed by a short bibliography, guiding an interested reader to some
relevantbooksandpapers.Insomeinstances,theoriginalpapersareincludedinthelist.No
attempthas,however,beenmadetogiveanexhaustivelistofreferences.Anumberofproblems
arealsogivenattheendofeachchapterforthestudentsincasethebookisfollowedasatext
foracourse.
I owe my gratitude to several individuals for their support and encouragement in the
preparationofthisbook.Firstandforemost,IthankMarlanScullyforhislongfriendshipand
manyfruitfulcollaborationsthathelpedshapemythinkingaboutaspectsofthefoundationsof
quantummechanics.ApersonmostresponsibleforthisbookisDavidLeewhofirstproposed
the idea and remained an enthusiastic supporter and inspiration throughout the writing of
thisbook.IamalsogratefultoPeterMcIntyrewhoseenthusiasticsupport,astheHeadofthe
Department,forteachinganunprecedentedcourseonquantummechanicstofreshmen,was
vitaltothisproject.RobertBrickandWenchaoGegraciouslyreadpartsofthebookandgave
me their unvarnished, but extremely helpful, comments. I also thank Jiru Liu and Chaofan
Zhoufortheirhelpwithproofreadingthemanuscript.SpecialthanksareduetoSonkeAdlung
andHarrietKonishioftheOxfordUniversityPressandCherylBrantofSPiGlobalforalltheir
helpduringthepublicationprocess.
FinallyIwishtoacknowledgethelovingsupportofmyfamilymembers,Sarah,Neo,Sahar,
Shani, Raheel, and Reema. My deepest gratitude is however reserved for my wife, Parveen.
Shehasbeenrelentlessinhersupportnotjustduringthewritingofthisbook,butforallthe
projects,bigandsmall,duringmylife.
M.SuhailZubairy
CollegeStation,Texas
October9,2019
OUPCORRECTEDPROOF – FINAL,10/3/2020,SPi
Contents
1 WhatisthisBookAbout? 1
1.1 FromClassicaltoQuantumMechanics 2
1.2 OutlineoftheBook 5
PARTI:INTRODUCTORYTOPICS 11
2 MathematicalBackground 13
2.1 ComplexNumbers 13
2.2 Trigonometry 16
2.3 VectorandScalarQuantities 20
2.4 ElementsofProbabilityTheory 25
3 ParticleDynamics 32
3.1 ClassicalTrajectory 32
3.2 LinearMomentum 35
3.3 KineticandPotentialEnergy 37
3.4 InelasticandElasticCollisions 39
3.5 AngularMotion 39
3.6 AngularMomentum 44
3.7 MotionofanElectroninElectricandMagneticFields 45
4 WaveTheory 50
4.1 WaveMotion 50
4.2 Young’sDouble-slitExperiment 57
4.3 Diffraction 61
4.4 RayleighCriterion 66
