140 CHAPTER8. RECTANGULARPOTENTIALS
andthetransmissioncoefficientisapproximately
T≈e−^4 Qa=exp[− 4√
2 m(V 0 −E)a/h ̄] (8.94)ThesituationissketchedinFigure[8.17].Mostoftheincomingwaveisreflected.
Intheclassicallyforbiddenregion,thewavefunctiondecaysexponentially. However,
sincethewidthoftheclassicallyforbiddenregionisfinite,thewavefunctionatthe
otherendofthebarrierisfinite,andsothereexistsatransmittedwave. Thismeans
thatnomatterhowhighthebarrierV 0 iscomparedtotheenergyEoftheincoming
particle,thereisalwayssomefiniteprobabilityfortheparticlestopenetratethrough
thebarrier.
Quantum-mechanically, asoapbubbleheadingforabrickwallhasafinite, al-
thoughexceedinglysmall,probabilityofbeingfoundontheotherside ofthebrick
wall.
Thefactthat aparticlecan penetrateapotentialbarrierwhoseheightexceeds
theenergyoftheparticleisknownas”Tunnelling”. Ithasimportantapplications
throughoutmodernphysics,e.g. inthestudyofsemiconductors,andofradioactive
decay.