Introductory Quantum Mechanics

903 Pages·2003·15.556 MB·English

by  Richard L. Liboff

1A LEGEND
HYDROGEN 1.0079
G.l* H 1 Name Symbol MassNumber
I
ts' Density(gmcm-3) MAGNESIUM/204.305
3.71 HEX 2A (CommonCrystalPhase)..........1.74 Mg 12r--AtomicNumber
U14T.H0IUM 6.9101410 BERYLLIUM 9.0122 Latti(cAe)Constant,a""- [Ne]3s2- ~AtomicConfiguration
O.A U 3 1.15 Be 4 MeltingTemperature_ 93,2221 HtEX 318t--MeanDebyeTemperature(LTSignifiesaLowTemperatureDetermination)
2 ls225' ls~,z (K) I
1.48 BeC 2.28 HEX CrystalType(CommonCrystalPhase)
453 400 1550 1000 FCC-Face-eenteredCubic ORC-Orthorhombic
SODIUM 22.9898 MAGNESIUM24.305 BeC-Body-eenteredCubic HEX -Hexagonal
0.17 Na 11 1.74 Mg 12 SC -SlmpleCublc DIA -Diamond
CUB-Cubic RHl-Rhombohedral
3 [Ne]3s' [Ne]3,z TET -Tetragonal MeL-Monoclinic .
4.23 BeC 3.21 HEX 38 48 58 8B 78 8
371.0 150 922 318
POTASSIUM 39.09 CALCIUM 40.06 SCANDIUM 44.956 mANIUM 47.90 VANADIUM 50.942 CHROMIUM 52.00 MANGANESE504.938 IRON 55.85 COBALT 58.93
0... K 18 1.14 Ca 20 2.. Se 21 4.51 TI 22 1.1 V 23 7.18 Cr 24 7.43 Mn 25 7." Fe 261.8 Co 27
4 [Ar]4s' [Ar]4s2 [Ar]3d'4s2 [Ar]3d24s2 [Ar]3ds4s2 [Ar]3cf54s1 ....[Ar]3d54,z [Ar]3cf14s2 [Ar]3d74,z
In BCC u. FCC 3,31 HEX 2.11 HEX 3.02 BeC 2M Bce CUB 2.17 BeC 2.51 HEX
337 100 1111 230 1812 359LT1933 380 2163 390 2130 460 1518 400 1808 420 1768 3B5
RUBIDIUM 85.47 STRONTIUM 87.62 YTTRIUM 88.91 ZIRCONIUM 91.22 NIOBIUM 92.91 MOlYBOENUM95.94 TECHNETIUM 98.91 RUTHENIUM 101.07 RHODIUM 102.90
1.u Rb 37 2.10 Sr 38 UI Y 3St•.• Zr 401.4 Nb 41 10.2 Mo 42 11.5 Tc 4312.2 Ru 44 12.4 Rh 45
5 [Kr]Ss' [Kr]s,z [Kr]4d'5s2 [Kr]4dZS,z [Krj4(145s' [Kr]4d55s' [Kr]4d5SS2 [Kr]4d7Ss' [Krj4deSs'
5,H BeC '.01 FCC 3M HEX 3,23 HEX 3.30 acc 3.11 acc 2.74 HEX 2.70 HEX 3.10 FCC
312 56LT 1043 14rtT1796 2setT212S 250 2741 275 2890 380 2445 2583 J82lT 2239 35()lT
CESIUM 132.91BARIUM 137.304 lANTHANUM 138.91 HAFNIUM 178.49 TANTAlUM 180.95 TUNGSTEN 183.85 RHENIUM 186.2 OSMIUM 190.20 IRIDIUM 192.22
(WOLFRAM)
1.10 C. 553.5 Sa 58'.17 La 57 13.1 Hf 721... Ta 7318.3 W 74 21.0 R. 75 22.1 Oa 7822.5 Ir rr
6 [Xe]6s' [Xe]6s2 [Xe]5~6s2 <lIlI [Xe]4"45cf6s2 [Xe)4f'45d3E),z [Xe]4f'4Sd~S2 [Xe)4f'45dS&S2 [Xe]4,,4Sd'6s2 [Xef4f'~d76s2
1.05 BeC 5.02 BeC 3.75 HEX 3.20 HEX 3,31 BeC 3.1' acc 2.76 HEX 2.74 HEX 3.14 FCC
302 4QlT998 110&-T 1193 132 2495 225 3683 310 3453 416LT3318 4()()lT2683 430
FRANCIUM 223 RADIUM 226 ACTINIUM 227
~
Fr 87 (5.0) Ra 88 10.1 Ac
7 [Rn]7s' [Rn]7s2 [Rn]6d'7s2
...
(BeC) 1.31 FCC
RAREEARTHS
[phone]
CERIUM 140.12 PRASEODYMIUM NEODYMIUM14-4.24PROMETHIUM 145 SAMARIUM 150.35
140.91
~ ~ 58~ ~ H~ ~ H ~ ~~ ~ ~
LANTHANIDES 6 [Xe]4fscfl6s2 [Xe]4f~£106s2 [Xe]4f4SdOSs2 [Xe]4f55cfl6s2 [Xe]4f'S(106,z
5.1' FCC 3.17 HEX 3." HEX '.00 RHL
1071 1JgLT1204 152LT 1283 15~T (1350) 1345 166
THORIUM 232.04 PROTACTINIUM231 URANIUM 238.03 NEPTUNIUM 237.05 PLUTONIUM 244
11.7 Th 80 15.4 Pa 81 18.07 U 82 20.3 Np 93 11.8 Pu M
ACTINIDES 7 [Rn]6d~s2 [Rn}Sf3&d'7s2 [Rn]SfSSdo7s2
5.oe FCC 2.15 ORC 4.72 ORC
2020 100 1470 1406
NOBLE
ELEMENTS
HELIUM 4.0026
0.171 He 2
152
3.17 HEX
3A 4A SA 6A 7A
-1.0(26Aim)26LT
BORON 10.81CARBON 12.01 NITROGEN 14.007 OXYGEN 15.999 FLUORINE 18.998NEON 20.18
1.1.
2.34 B 5 2.21. C 8 1.03 N 7 1.43 0 8 U7{a) F 8 Ne 10
1522r2p' ls22s~ ls22r2p3 lr2s~4 1$~s22p5 ls22522'"
..73 TET 3.17 DIA 4.031 HEX 1.13 CUB Mel 4,43 FCC
2600 1250 (4300) 1860 63.3 (~)7g..T 54.7 (y)46LT53.S 24.5 63
ALUMINUM 26.982 SILICON 28.086 PHOSPHORUS30.974SULFUR 32.084 CHLORINE 35.453 ARGON 39.iW8
2.70 AI 13 2,33 SI 141.82(.....)P 15 2.07 S 18 2.oe CI 17 1.71 Ar 1.
. [Ne]3s23p' [Ne]3s23p2 [Ne]3s23p3 [Ne]3s23p4 [Ne]3s23p5 [Ne]3s23p'
1B 2B 4.01 FCC 1.43 DIA 7.17 CUB 10.47 ORC 21."•. 1.24 ORC 01..7312'4I.• FCC
933 394 1683 625 317.3 386 172.2 83.9 85
.N.I.CKEL 58.71 COPPER 63.55 ZINC 65.38 GAllIUM 69.72 GERMANIUM 72.59 ARSENIC 74.922 SELENIUM 78.96 BROMINE 79.91 KRYPTON 83.80
HI 28 .... Cu 28 7.14 Zn 30 U1 Ga 31 l.az Ge 32 1.72 Aa 33 4.71 se 34 4.10 Br 35 3.07 Kr 31
[Ar}3d'4s2 [Ar]3d,04s1 [Ar]3d,04s2 [Ar]3d104s23p' [Ar)3d,04r4'' [Ar]3d,04r4p3 [Ar)3d,04s24Jt [Ar]3d,04s24p5 [Ar]3d'04s24p'
3.12 FCC 3.11 FCC 2.• HEX 4.11 ORC I.• DIA 4.13 RHL 4.11 HEX •.17 ORC 5.72 FCC
1726~ 375 1356 315 893 234 303 240 1211 360 1090 285 490 15QlT 266 116.5 73LT
PAlLADIUM 106.40SILVER 107.87CADMIUM 112.40 INDIUM 114.82TIN 118.69 ANTIMONY 121.75TELLURIUM 127.60 IODINE 126.90XENON 131.30
12.0 Pd 4I1o.a Ag 47 .... Cd 41 7.31 In 49 7.30 Sn 50 U2 Sb 51 1.24 Te 52 4JM I 53 3.77 Xe 54
[Kr]4d,05so [Kr]4d'OSs' [Kr]4d105s2 [Kr]4dl05s~p' [Kr)4d'OSs25" [Kr]4d1OSs25p3 [Kr}4d'05rSp4 [Kr]4dl05s~p5 [Kr]4d'OSS25p'
3. FCC 4.oe FCC 2.• HEX 4.H TET 1.12 TET 4.11 RHl 4.... HEX 7Z7 ORC '.20 FCC
1825 275 1234 215 594 120 429.8 129 505 170 904 200 723 l:J9lT 387 161.3 5SLT
PLATINUM 195.09GOlD 196.97 MERCURY 200.59 THALLIUM 204.31 lEAD 207.19 BISMUTH 208.98 POlONIUM 210 ASTATINE 210 RADON 222
21.4 PI 7811.3 Au 78 13.' Hg 80 11.11 T1 81 11.4 Pb 82.., BI 831.4 Po 84 At 85 (4,4) An 81
[Xe]4f145d'OSso (Xe]4fI4Sd1OSs' [Xe]4f14Sd'OSS2 [Xe]4f'45d'OSs2E)p' [Xe}4f'4Sd1OSs2E)p2 [Xe]4f'45d'OSs2Eip3 [Xe]4f'45dlOSS~Jt [Xe]4fI45d'OSs~p5 [Xe]4fI45d'OSs~'"
3.12 FCC 4.oe FCC 2.• RHl 3M HEX 4.11 FCC 4.75 RHL 3.35 SC (FCC)
2045 230 1337 170 234.3 100 sn 96 601 88 544.S 120 S27 (57S) (202)
EUROPIUM 151.96GADOLINIUM 151.25TERBIUM 158.92 DYSPROSIUM162.50 HOlMIUM 164.93 ERBIUM 187.26THULIUM 168.93 YTTERBIUM 173.04 LUTETIUM 174.97
7.10 Eu 53 1.23 Get 84 1.54 Tb 15 '.71 Dy 66 '.01 Ho 67 1.37 Er 68 1.31 Tm 68 1.17 Vb 70 ..,4 Lu 71
[Xe)4f7SdOSr [Xe)4f7Sd16s2 [Xe)4f1l5dOSs2 [Xe]4f,oSdOSs2 [Xe]4f115~6r [Xe]4f12SdOSs2 [Xe]4r~do6s2 [Xe)4"45~6s2 [Xe}4f'4Sd'6s2
4.11 BeC 3..14 HEX 1.80 HEX 3.51 HEX U8 HEX 3.1. HEX 3.14 HEX I.• FCC 3.51 HEX
1095 10rLT 1585 1761.T 1633 1~T 1680 186LT1743 191LT1795 195LT1818 2O()lT1097 llBlT1929 207LT
AMERICIUM 243 CURIUM 247 BERKELIUM 241 CAliFORNIUM 251 EINSTEINIUM 254 FERMIUM 257 MENDELEVIUM 256 NOBELIUM 254 LAWRENCIUM 257
11.' Am 85 Cm 88 Bk 87 Cf 81 e- 88 Fm 100 Md 101 No 102 Lw 103
[Rn]Sf76cJ&7s2 [Rn}5f76cJ17s2 [Rn]5f76d~s2 [Rn]5faad'7r
1267 1600
INTRODUCTORY
QUANTUM MECHANICS
FOURTH EDITION
Richard L. Liboff
DistinguishedProfessorofPhysics
University ofCentral Florida
A
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www.aw-bc.com/physics
"I donotknow what Imayappear tothe world;buttomyselfIseem
to have been only like a boy playing on the seashore,and diverting
myselfinnow and then findingasmootherpebble or aprettiershell
than ordinary, whilst the great ocean of truth lay all undiscovered
before me."
This statement by Isaac Newton shortly before his death in 1727 eloquently
reflectsthesentimentsofallmaturescientistsfrom theancient pasttothepresent.
ToMyra
"She openeth hermouth with wisdom; and inhertongue isthelawof
kindness...."
Preface
Since earlier editions of this text, it remains the case that physics continues to
evolveinesoteric andpragmatic directions.In thepresent edition, anewchapter
addressing quantum computing has been added that well represents this theme,
as quantum computing is founded on basic elements of quantum mechanics but
isthought torepresentanewconcept forcomputers.Components ofthischapter
include:BinaryNumbers;LogicGates;TuringMachineandComplexity Classes;
Qubits and Quantum Logic Gates. The chapter concludes with a description of
Grover'salgorithm, whichcomes intoplayinthe 'searchproblem.'
Twenty seven problems are included in this new chapter, many of which, in
thespirit ofearlier editions, carry solutions.Some ofthe topics included inthese
problems are: Classical and quantum logic gates, Boolian relations, Factoring
problemsandEuclid'salgorithm.Thereareatotalof870problems inthisedition.
AnewappendixisincludedinthiseditionthatdescribestheHarmonicOscilla
torinSpherical Coordinates andanumber ofinsertsareincluded intheappendix
onPhysical Constants andEquivalence Relations.
Atotalofninenewproblemshasbeenadded topreviouschapters thataddress
inpart: Properties of thecommutator,reduced formof thesquare ofangular mo
mentum, parallel relations forthecubical quantum box,quantum confinement.
A number of corrections have been made throughout the text, mostly due to
input from studentsand teachers throughout the world, whose suggestions Itake
pleasure inacknowledging.
I take this opportunity to express my deep gratitude to the many individuals
throughout the world whohavecommunicatedwithmeregarding typos andsug
gestions for this text. More locally,in addition to all other colleagues who have
contributedtothesuccessofthisbook,thefollowingindividualshaveprovedtobe
ofinvaluable assistance inpreparation of this newedition: TobyBerger,Bradley
Minch, Rajit Manohar, Eric Sakk, Ian Rippke, Brian E. Moritti, James Snyder,
Andy Martwick, and IgorDevetak.My special thanks goes toDavidMermin for
hisexpertassistance inthepreparation ofthenewchapter.
Itismypleasure alsotodeclareagainmyappreciation tothemanyindividuals
whohavetaught from prioreditions ofthis workandthemanywhohaveleamed
from it. I trust that these kind individuals will findthis new edition equally re
warding.
Ithaca,2002 R.L.Liboff
lY'~?~,n
v
Piping down thevalleys wild,
Piping songs ofpleasantglee,
Onacloud Isawachild,
Andhelaughing said tome;
"Pipe asongabout aLamb!"
SoIpipedwithmerry chear.
"Piper,pipe thatsong again;"
SoIpiped; hewept tohear.
"Drop thypipe, thyhappypipe;
Sing thysongs ofhappy chear;"
SoIsung thesameagain,
While hewept withjoytohear.
"Piper,sittheedown and write
Inabook, thatallmay read."
So hevanish'dfrom mysight,
AndIpluck'dahollow reed,
AndImadearuralpen,
AndIstain'dthewater clear,
AndIwrotemyhappy songs
Every childmayjoy tohear.
Introduction toSongs ofInnocence
-WilliamBlake(1757-1827)
Contents
Preface vii
Topical Problems xvii
PART I • ELEMENTARY PRINCIPLES AND APPLICATIONS TO
PROBLEMS IN ONE DIMENSION 1
1 • Reviewof Concepts of Classical Mechanics 3
1.1 Generalizedor"Good"Coordinates 3
1.2 Energy,theHamiltonian,and AngularMomentum 6
1.3 The State ofaSystem 19
1.4 Propertiesofthe One-DimensionalPotential Function 24
2 • Historical Review: Experiments andTheories 30
2.1 Dates 30
2.2 The WorkofPlanck. Blackbody Radiation 31
2.3 The WorkofEinstein. The PhotoelectricEffect 36
2.4 The WorkofBohr.AQuantum Theory ofAtomic States 39
2.5 Wavesversus Particles 43
2.6 The deBroglie Hypothesisand theDavisson-Germer
Experiment 46
2.7 The WorkofHeisenberg. UncertaintyasaCornerstone ofNatural
Law 53
2.8 The WorkofBorn.ProbabilityWaves 55
2.9 SemiphilosophicalEpiloguetoChapter2 57