199
Inatomicphysics,theintegervaluesofthelquantumnumberareassignedletters,
namely:
l = 0 S
l = 1 P
l = 2 D
l = 3 F (12.43)
Beyond l = 3, the assignment is alphabetical, i.e. l = 3 , 4 , 5 , 6 ...correspondto
”F,G,H,I...” respectively(the reasons forthese letter assignments goback to the
historyofspectroscopy,andneednotconcernushere.)^2 Thusthe{nlm}={ 100 }
stateisreferredtoasthe”1S”state;the{nlm}={ 21 m}statesarereferredtoas
the”2P”states,andsoon,asindicatedinFig. [12.1].
Wenowusetheformulasineq. (12.36)tocalculatethe 1 Sand 2 Swavefunctions
explicitly.
- The1SGroundState Sincejs=n−l− 1 ≥0,thesmallestpossiblevaluefor
nisn=1,whichimpliesthatl=m=0.Thisisthelowestenergystate,or”ground
state”ofthe hydrogenatom; itisthestatewherethe bindingenergy isgreatest.
Accordingto(12.36)wehave
φ 100 = N
u 10 (2r/a 0 )
r
Y 00
=
N
√
4 π
u 10 (2r/a 0 )
r
(12.44)
where
u 10 (ρ) = e−ρ/^2 ρF 10 (ρ)
= e−ρ/^2 ρ
1 −∑ 0 − 1
j=0
cjρj
= e−ρ/^2 ρ (12.45)
Therefore
φ 100 =
N
√
4 π
2
a 0
e−r/a^0 (12.46)
(^2) ”S”standsforthe”sharp”seriesofspectrallines,”P”standsforthe”principal”series,”D”for
”diffuse”and”F”for”fundamental.”