Download Mathematical Methods for Physics I - Problems with Solutions | PHYS 6124 and more Study notes Physics in PDF only on Docsity! rhe Seeuler Sundin “is, oot [A-AT]= (2-2)?
=> Ths eagen values ore. desde ay=a- Coley enarett )
The eigenvaluo epustion yields.
XM =O > BaD. TY+B =o
=> en (4 J (only ome elpemueetor ).
0
/
a
for combnrente2 , we Chesse . z= (1)
o
37° dim ther (A-XL) = |
ker (A-AlL) % the <ifen Spee fr thd ep enetee Xr.
The generoh'zeol An efenpace A Ker £eq Xr)"] woth
the corresponding Seutltar- epnaction > lot /A 2) = Ct-ADG LED
=? Ker (A~AL) CkerllA ALY IC ~-- C kerlt4-X2)]
For th's Case Me cannet drewe dm Cker(CtArAL1)I=3, Se
extend @ to a basis of ker Lca-AL)*] given 4, ae (ee,
find Seek. a>.
= l
Let A= (< | «Mow, ker FCA-X1)?] muse Be Re
0
$0 extend Fad & te a basis of Te hy, for crample,
=. f°
“@)
e
Novo madly thls basis by replacing 6. hy
=> bro 0
B's ADE = (os Me)el)
ie =|
= _ ane | { ©o 0
@'= (A-AL) B= CA-ALYS, = -/'\.
; oO oY ! -{
“tomp =p FAH
0
> g’ stiitt ives a basis of ker (A-~XI ) ancl a a! to.
SH 91V8 a asks ef ker Ltdary*J. Se ay E andl 2
give a basts of TR?
1 0 0
Ferm +42 mathe ; Pe cee! By a \ o|
oO -1 |
apy. fi & @
rs I : |
i { |
rg
>rsqy-f 5 ®
Ss ~~ a
s 0 hy
*
Applying the = normalized erithog ral cond tlon,
cs] CmITS]= I
= emth )s* =| = i
> amp = => Nant JA
ee} = te
Gm 24m" yal=] C= Kam
* = =
Noon + Re
—_ Le 1 5
= S Norn Nam 2m ABE j
Sls iL ,
php “ham Ys
mp me
S3 — Nemt Se
wort 0 _ an ,
Mm +a
Woh Ys Otbt . i= Ca. Sm (3k 4 +02) ; WG Stnlit eibey]
The - normed re odes.
O O 0
(t)
pure translation
(L) The too mosses and 2 are moving teyether, The mass 3 A stationary
+
(B) The too masses 3 and d sare moving ta gesker. The mass / ¥
proving along Ene Same difeetiin at mesa,
“Pablene
a) mt" 4 Sy amy) =O
Cy" tla sult ay ye ©
Because a9 ot ye aol . 4 SNe Do : 4" y= >
=D) C=O
he. ye yas yl 2% =o
Define
ry ape ey pe
oF 9) hey Bp’
by . -~ | °
det \Aa-AT| = “[ -r | |
x
a3 by
= 7 (-A)-2 -SAzS
=p UDC 8 be, AeA? oA As>72-|
at
len Net
sae
Ayo -y =D rt
whew d=.
). ned an parma orm
-2 Oo d | \ \
he SASt}o A | S=[-2 4 0
