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'iel. e ha*e ne#lecte the e''ects ue to s"in an#ular momentum o'the electron . (reat 1H as a "erturbation an sho$ )0( =ls statesare not s"lit $here as )1( =lp states are s"lit into three statesse"arate b+ the ener#+ inter*al BB . (his is )no$n as normal

eeman E''ect6. n continuation o' the "re*ious "roblem i' $e ta)e into account thes"in an#ular momentum o' the electron the amiltonian $ill be o' the

'orm o' the 'orm ][2

,)(,21210 zz

gSLm

eBHSLrfHHHHH +==++= .

ere the secon term re"resents the s"in!orbit interaction an thethir term re"resents the interaction $ith the ma#netic 'iel. 7ssumethat the e''ect o' 2H is small com"are to e''ect o' 1H use the$a*e'unctions corres"onin# to 1H as the "erturbation to calculatethe e''ect o' 2H . (his is )no$n as $ea) 'iel anomalous eeman

e''ect or 8ust the eeman e''ect.9. n the 'ollo$in# "roblem $e $ill consier the e''ect o' "roton

ma#netic moment an hence the h+"er'ine structure. Since electronan "roton are s"in "article thus there are 'our "ossible s"in

states namel+ pepepepe ,|,,|,,|,,| . Sho$ that the

o"erator ]1[2

1peP += is the s"in e&chan#e o"erator i.e. $hen P

o"erates on an+ state the s"in irections are e&chan#e = pepeP || etc. (he pe & re"resent the Pauli s"in matrices 'or electron an"roton res"ecti*el+ an the+ $or) onl+ on the electron an "roton"art o' the $a*e'unction res"ecti*el+.

;. Calculate the "robabilit+ o' e&citation to the p2 state o' a h+ro#enatom ori#inall+ in the #roun state ue to a homo#enous electric 'iel

$ith time e"enence22

0

+

=

t

EE . Discuss the limits i' small an

lar#e *alues o' an their si#ni'icance.