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Chapter 3 The Wave-like Behavior of Electrons Truthisstrangerthanfiction,butitisbecausefictionisobligedtosticktopossibilities; t ...
36 CHAPTER3. THEWAVE-LIKEBEHAVIOROFELECTRONS 3.1 Wave Equation for de Broglie Waves Wherethereisawave,thereisawavefunction. Thew ...
3.1. WAVEEQUATIONFORDEBROGLIEWAVES 37 Thesameresultisobtained,ofcourse,forthecosine.Thisexpressionfortheenergy ofanon-relativist ...
38 CHAPTER3. THEWAVE-LIKEBEHAVIOROFELECTRONS 3.2 The Double-Slit Experiment Weconsiderabeamofelectronswhich,afteraccellerationac ...
3.2. THEDOUBLE-SLITEXPERIMENT 39 whereθistheangle,relativetothex-axis,fromthecenterofthebarriertothepoint yonthescreen. Nowthein ...
40 CHAPTER3. THEWAVE-LIKEBEHAVIOROFELECTRONS Butinorderforanelectrontopassthroughasmallregionofthescreensometime intheintervalt= ...
3.3. DOELECTRONSTRAVELALONGTRAJECTORIES? 41 TheBornInterpretation Denote the wavefunction associated with an electron by ψ(x,y,z ...
42 CHAPTER3. THEWAVE-LIKEBEHAVIOROFELECTRONS NowtheprobabilitiesPA(y)andPB(y)arenearlyconstantfordetectorsplaced inasizableregio ...
3.3. DOELECTRONSTRAVELALONGTRAJECTORIES? 43 Brogliewavewhichhadexpandedtoseveralcentimetersacrosswasintenseenough totriggerevena ...
44 CHAPTER3. THEWAVE-LIKEBEHAVIOROFELECTRONS ...
Chapter 4 The Quantum State Wetakeforgrantedtheideathateveryobject,ateverymomentintime,iscenteredat adefinitepointinthree-dimens ...
46 CHAPTER4. THEQUANTUMSTATE LetusimaginesubdividingthelengthofthepipeintoNequalintervalsoflength !=L/N, asshowninFig. [4.2]. If ...
4.1. ANEWREPRESENTATIONOFMOTION 47 = a b 0... 0 (4.4) whichseemstosuggestthatthepartic ...
48 CHAPTER4. THEQUANTUMSTATE vector.Ifthecomponentsof%varerealnumbers,thisisgivenby %v·%v = [v 1 ,v 2 ,v 3 ...,vN] ...
4.2. HILBERTSPACE 49 andthisistheendofthedigression. Returningtothe”BornInterpretation”ofthevectorψ%(or”|ψ>”),weseethat theto ...
50 CHAPTER4. THEQUANTUMSTATE oftheindexiinsomerangei= 1 , 2 ,...,N.Butafunctionfisalsoasetofnumbers labeledbyanindex.Thereisonen ...
4.2. HILBERTSPACE 51 f(x),−∞<x<∞representthe”components”of|f>,andf∗(x)representsthe componentsofthecorrespondingbra< ...
52 CHAPTER4. THEQUANTUMSTATE 4.3 The Dirac Delta Function Ifthelinearoperation f′(x)= ∫∞ −∞ dyO(x,y)f(y) (4.33) isanalogoustomat ...
4.3. THEDIRACDELTAFUNCTION 53 Itisreasonabletoaskwhyoneshouldgotothetroubleofintroducingsequences. WhynottaketheL→∞limitrightawa ...
54 CHAPTER4. THEQUANTUMSTATE Theresult(4.45)establishesthatthesequenceofgaussians(4.40)isadeltasequence: δ(x−y)= lim L→∞ √ L π e ...
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