Chapter 3
The Wave-like Behavior of
Electrons
Truthisstrangerthanfiction,butitisbecausefictionisobligedtosticktopossibilities;
truthisn’t.
- MarkTwain
Matterinthesolidstateconsistsof atomsinaregular(”crystalline”) arrayof
somekind,andtheatomicstructureofsolidsisdeterminedbyX-raydiffraction.X-
rays,beingaformofwavemotion,reflectofftheatomsinthearray,andinterfereto
formapatternwhichcanbecalculatedfromtheprinciplesofphysicaloptics,givena
knowlegeofthestructureofthearray,andthewavelengthoftheX-rays.Theinverse
problem,findingthestructureofthearraygiventheX-rayinterferencepattern,is
thesubjectofX-raycrystallography.
In 1927 DavissonandGermer,inanefforttocheckDeBroglie’shypothesisthat
electronsareassociatedwithwavemotion,directedabeamofelectronsatthesurface
ofcrystallinenickel.Theelectronswerereflectedatvariousangles,anditwasfound
that theintensity ofthe reflectedelectrons, as afunction ofreflectionangle, was
identicaltotheinterferencepatternthatwouldbeformedifthebeamwereinstead
composed of X-rays. Assuming that the electron beam was indeed some sortof
wave,thewavelengthcouldbedeterminedfromtheintensitypatternofthereflected
electrons. The wavelength λ was found to equal, within experimentalerror, the
deBrogliepredictionλ=h/p, wherepistheelectronmomentum,determinedby
accelleratingtheincidentbeamofelectronsacrossaknownpotentialV.Apartfrom
brilliantlyconfirmingtheexistenceof”deBrogliewaves”,thisisanexperimentwith
extraordinaryandprofoundimplications. Todiscusstheseimplications,itisuseful
toconsideranexperimentalsetuplesscomplicatedthanthatusedbyDavissonand
Germer,inwhichtheelectronsaredirectedataninpenetrablebarriercontainingtwo,
verynarrow,slits. First,however,weneedanexpressionforthewavefunctionofde
Brogliewaves.