Download Handwritten Notes on Degenerate Perturbation Theory | PHYS 422 and more Study notes Physics in PDF only on Docsity! ‘Degenerate Perhurbahou, Theory | Coenarah Case
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whwe he awrgy 2 s+ eiggwalues Cl, Ho ave. noun , In the
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aiggstate, Gorwrically , (alrelling ee eroryy vel by 2,
lol rer, steses
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hare is ony oe ary Sepavaue Tor Ho + €
hist ate sigarsledes we above aabar,
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2S = i-2). /
“the geasral sche ia Parhubahas Heong involues hadiag, he
exoct skates:
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Wa sees Solutions
Ena> EO 4 XE , Vem a.
(2)
d= dar] B ci buy © MBH f
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Note Hak xe un perhoted port dy hea. Haga stece is a sum over all
igunstedes for that level. Addi welwe |
dy tee us perhubed tigpgitles 10° orarais aually
Hie orthogonalihy req unremant Lor [Ma OD.
60 OPA) = oO j4o . i
Substhabag into ly gives
\fuvrts] yh f Zetactey MAM EW j
= (Ens 2E1-)b yf CeeycOy 4% 1G e- f |
~ Cy up = EG = wp EA
“Tus tee mothod reduces to:
if possible choose. a > fo be acgorstates of, Hi, |
‘he eigenvalues oe E,".
Example. Tor he spin~ ‘he cag, tt He = et
By =. Voy
we nde ta ony pair dh otedes Ley Ly ae
orkeogaal, 2eqgnstedes ah Ao Whide will be egenstales
ah.
Answer: The. eigusteles of K, ave HK > ond 1+, To check
fib = V dy BD = VEBD
Wyte) = ce ee 2 -\bs
Alas we should have chosen Wr?) - ED
ua = 1-&S
Than the wo frstarde eagy comecKus ave £4 and
Bp e-V. Tuva 40 fist oder
E,= €-v
E.= € +V
Solukorn methed 2 (eigenvoluss d Mi).
Rehaning fo @ a we d&ne te mabix
(Hg = Cay & pile, 1°
then we geF
S(H)jec = B®
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Gj
Weihag US exphety gives -
wt ~ ~t \
Hy Hin He. q “|
Ha Har Ha ++ C2 Cz
Nn on
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Her Hex Hes ~~ - Cs
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Aes eo protod ts
Tom Ay = Sec | Haney >
2) “Tho. Fist order orgs cortedtions ake agenvelua Qh Hi
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Examples in ie example of ha start dh due adles.
A iN A A
We 2b > H, =V Ox
ond fo the wnperrybed CO
Enos Sales
E,-¢€ HOD = FED NW OD=(-E>.
Delernune. Hy ond Hae xigowalues o, Hus.
Anew Hy = <a PUA [Bed
= ELA ES = V G2 (GND
map \y (2) (°: (:) =O
\ oa
Bae 6 P1109 = v GalEla>
WN UO) ON
Noe tat Ra= (42 { A 1€,>
‘ tv +
~ ke, Hy |e)! =v =V
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Sally ong con Shag Hn =O
