Advanced undergraduate quantum mechanics

612 Pages·2018·3.327 MB·English

by  Deych, Lev I

Lev I. Deych
Advanced
Undergraduate
Quantum
Mechanics
Methods and Applications
Advanced Undergraduate Quantum Mechanics
Lev I. Deych
Advanced Undergraduate
Quantum Mechanics
Methods and Applications
123
LevI.Deych
PhysicsDepartment
QueensCollegeandtheGraduateCenter
CityUniversityofNewYork
NewYork,NY,USA
ISBN978-3-319-71549-0 ISBN978-3-319-71550-6 (eBook)
https://doi.org/10.1007/978-3-319-71550-6
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ToYelena,Daniil,Sergei,andmydogXena
Preface
Themarketforundergraduatetextbooksonquantummechanicsisoversaturatedas
one can literally choose from tens, if not hundreds, of different titles, with several
ofthembeingacceptedasastandard.Writingyetanothertextbookonthissubject
mightappearasarecklessandtime-consumingadventure,andwhoevergotengaged
in it can be rightfully suspected in arrogance and self-aggrandizement. Be that as
it may, after 15 years of teaching an undergraduate quantum mechanics course at
Queens College of the City University of New York, I finally came to realization
that neither I nor my students are particularly happy with the existing standards.
It also occurred to me that my approaches to teaching various topics in quantum
mechanics,alongwiththelecturenotesIhaveaccumulatedovertheseyears,could
form the foundation of atextbook that would be different from those Isaw on the
market.Inmanycases,studentstreattheirphysicstextbooksasareferencesource
for formulas and postulates—used to solve problems rather than as actual reading
material.I,ontheotherhand,dreamedaboutwritingabookthatwouldactuallybe
read;andinordertoachievethat,Ihavedevotedasignificantamountoftimetothe
explanation of the most minute technical details of various technical derivations.
The level of technical detail in the book would ideally allow students to use it
without the need for a lecturer’s explanations, allowing professors to use precious
lecturetimeonsomethingmoreproductiveandfun.Butquantummechanicsisnot
just about derivations of formulas (though these might be fun, of course, for the
mathematicallyinclined).Thephysicalcontentofthederivedresultsisimmensely
more important and interesting, if you ask me. Thus, I have included in the text
extensive qualitative discussions of the physical significance of derived formulas
andequations.Finally,tomakereadingevenmoreenjoyable,Itriedtopreservethe
informal, colloquial style of my lectures, addressing readers directly and avoiding
thedry,impersonalmannerfoundintoomanyformalscientifictexts.
Mostphysicstextbookspresentideasandconceptswithoutmorethanapassing
mentionofthepeoplewhodiscoveredthem.Suchanapproachaimstoemphasize
the objectivity of the laws and principles that physics deals with. The essence of
theselawsdoesnotdependonthepersonaltraitsandideologiesoftheirdiscoverers,
whichisnotalwaysthecaseinhumanities.WhileIagreethatsuchacold,formal
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x Preface
approachisjustifiedbytheobjectivenatureofthelawsofphysics,Iamstillnotsure
thatitisthebestwaytopresentthematerialtostudents.Thisapproachdehumanizes
physics,preventingpeoplefromrelatingtoitonapersonallevelandseeingphysics
as part of the general human experience. In this book, I tried to break out of this
tradition and introduced some personal details about the lives of those scientists
whowereresponsiblefordevelopingquantumtheoryandchangingourviewsofthe
universealongtheway.Iwouldlikethereaderstoseethatthecomplextechnicaland
philosophicalideasinquantummechanicsweregeneratedbymortalhumanbeings
withstrengthsandweaknesses—thattheyexperiencedstrugglesandmademistakes
forwhichtheyhadtobearfullresponsibility.Obviously,itwouldbeimpossibleto
talkaboutallthesegreat(andsometimesnotsogreat)men1indetail.Butwhenever
possible,Ihavetriedtoprovidebitsandpiecesaboutthepersonallivesofscientists
whosenamesappearinthetext.
Anyone writing a textbook on such an immense subject as quantum mechanics
alwaysstruggleswiththequestionofwhichtopicstoincludeandwhichtoleaveout.
There are, of course, some standard concepts that cannot be avoided, but beyond
those,thechoiceisalwaysafunctionoftheauthor’spersonalpredilections.These
predilections led me to include some topics that are not usually covered in under-
graduate textbooks, such as the Heisenberg equations, the transfer-matrix method
forone-dimensionalproblems,opticaltransitionsinsemiconductors,Landaulevels,
andtheHallconductivity.Atthesametime,IleftoutsuchpopulartopicsasWKB
andvariational methods. Thetotalcontents ofthebookwerechosen tosatisfythe
needs of a two-semester course for students who have already been exposed to
some quantum ideas in a modern physics course or its equivalent. At the same
time, the book can also be used for a one-semester course. While each instructor
decidingtoadoptthisbookcanchoosewhatevermaterialtheypreferfortheirone-
semestercourse,mysuggestionwouldbetoincludeChaps.1through9,aswellas
Chaps.11and15,whichcanbetaughtalmostindependentlyofotherchaptersofthe
book.(Whiletherearesomecross-referencesbetweentheseandotherchapters,they
shouldn’timpedethestudent’sorinstructor’sabilitytogetthroughthearguments.)
Finally, I would like to emphasize that the problems offered for solution by the
studentsareanintegralpartofthetextandmustbetreatedassuch.
Quantummechanicsisoneoftheultimatetriumphsofthehumanmind.Ienjoyed
writing this book, trying to convey the awesomeness of quantum ideas and of the
peoplewhocontributedtotheirdevelopment,andIhopethatyouwillenjoyreading
1Needlesstosay,atthetimeofbirthofquantumphysics,mostofthescientistswere,indeed,men.
Evenmoreremarkableareachievementsofafewwomenwholefttheirmarksonthetwentieth-
century physics. Nobel Prize winners Marie and Irene Curie have since become household
names,butotherfemalescientistssuchasGermanmathematicianEmmyNoetherandAustrian-
Swedish experimental physicist Lise Meitner also deserve to be remembered. Unfortunately,
the contributions of Noether, who uncovered the intimate relationship between symmetries and
conservationlaws,andMeitner,whotogetherwithOttoHahndiscoveredthefusionofuranium,
aretooadvancedforanintroductoryquantummechanicsbook,preventingmefromtalkingabout
thesescientistsinmoredetail.
Preface xi
it.Whilephysicsstudents,unliketheirbrethrenfromhumanitydepartments,arenot
accustomedtoactuallyreadingtheirassignedtexts,Iwouldliketoencourageyou
to overcome the established habits and give this book a chance. Who knows, you
mightlikeit.
NewYork,NY,USA LevI.Deych
Acknowledgments
IwouldliketothankDrs.MishaktulBhattacharyaandAlexeyTsvelikforreading
andcommentingontheportionsofthemanuscriptandforgeneralencouragement
andProf.NathanielKnightformakingsurethatmyhistoricalintroductiondidnot
deviate too much from actual historical facts. My special gratitude, however, goes
to Prof. Lev Murokh of Queens College for test-driving the book in a quantum
mechanicsclasshewasteachinginfall2017andfordiscoveringmultiplemisprints
and quite a few errors, thereby saving me from a great deal of embarrassment.
However, I take full responsibility for whatever mistakes might still remain in the
textandwillbeimmenselygratefultoanyonepointingthemouttome.
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