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SoRurditlof olifoltor 2e'l 2c:tl ?r'\lerq 2,lLl - Ch2 Cort siJer d one ol ;mer7S r uno,l "= [4(x *ip) 2h @ 3 ;rap lq ho r*o(t t c osei tla.fclr df n rt) "ln a, ln =Wx-ip) : ,l , ln-r> a) tfe valuen ,/ x ",*rt p inb"m s -! oh, buerrnl o(rrafors in@rms -{ the tais'nJ*'a x- E* (o+ ot) P = lry Co*dt) ='fu E rn l"l">+{,nldtln{ WrEr, n-t+,Er6r"n-,) L\ry- fnE^,o-&-ffi,t : tl% @ { rvt I n - j>+{i, r rl*, Click to buy NOW! P D F - X C h a n g e V i e w e r w w w . d o c u - t ra c k . c o m Click to buy NOW! P D F - X C h a n g e V i e w e r w w w . d o c u - t ra c k . c o m Click to buy NOW! P D F - X C h a n g e V i e w e r w w w . d o c u - t ra c k . c o m Click to buy NOW! P D F - X C h a n g e V i e w e r w w w . d o c u - t ra c k . c o m Click to BUY NOW! P D F - X C ha n g e Ed i t o r w w w . t r ac ke r - s o f t w a r e . c o m Click to BUY NOW! P D F - X C ha n g e Ed i t o r w w w . t r ac ke r - s o f t w a r e . c o m

Solution CH2 Problem 2.14Sakurai, Napolitanio 2ed, Modern Quantum Mechanics

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Solution to problem 2,14 CH2, Modern quantum mechanics 2nd edition by Sakurai and Napolitano

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Page 1: Solution CH2 Problem 2.14Sakurai, Napolitanio 2ed, Modern Quantum Mechanics

SoRurditlof olifoltor 2e'l 2c:tl

?r'\lerq 2,lLl - Ch2

Cort siJer d one ol ;mer7S r uno,l

"= [4(x *ip)2h

@3 ;rap lq ho r*o(t t c osei tla.fclr

df

n rt) "lna, ln

=Wx-ip): ,l , ln-r>

a) tfe valuen ,/ x ",*rt p inb"m s -! oh,

buerrnl o(rrafors in@rms -{ the tais'nJ*'a

x- E* (o+ ot)P = lry Co*dt)

='fu E rn l"l">+{,nldtln{

WrEr, n-t+,Er6r"n-,)L\ry- fnE^,o-&-ffi,t

: tl% @ { rvt I n - j>+{i, r rl*,

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Page 2: Solution CH2 Problem 2.14Sakurai, Napolitanio 2ed, Modern Quantum Mechanics

Sr e'Yt'L,1.

(a, o')(o + et) = a2 +ad+ cf a n d'

Pr*b L. ^ 2,111 LH 2 * Soteu'oi bt\

Step L+

-* lxpln > = I *;L \[ru <tvvt!Gra+)(a-o|ln>

= @)G -lo "l n > l< "' \nctf n > + <m laLl tl t - I m t"r1r,

a -L?LS-.n

: _LhS n,n

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Page 3: Solution CH2 Problem 2.14Sakurai, Napolitanio 2ed, Modern Quantum Mechanics

{ ?r"blr* <Hz- 2,r.{)G{,54D eVb) ile tn*//<

e./h@)=t$n,eJ).(*)Rrf |a,ce, Q - y.P fltert vre |ef

#@)=+(G,vtt)*W)frs fhtrc h r) o tine )eyer,"l*,rtrl x ,"r) p *p/ivtg

,)/'|frQr)-+ (fa yyr)

/uw cdnsirler Cfr, ryJ

Iu,ytrJ =lH,xlr*xfu,pJL/ q ha ra Sfa/nr! aru) re)c. lrtfu x]=4

rr1

[u-pJ= Lh *qYUsll/G the-s< vol rell ^-u7,et[t".fJ= -ifr( +yifrdprTl '--w

s .^ b gr i fu6ry .rh, v ol,rut -/ fn . xfJ ),r eluo&ion?..{!#

{ ?r}=+f*(Pr*Lr("#,J-t t = er-*(r/Y-t=7--\- dx /=r9 (*p:2(r>_+#

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Page 4: Solution CH2 Problem 2.14Sakurai, Napolitanio 2ed, Modern Quantum Mechanics

A"rnr

:9 e*>:o'lhls ; bl/rel virr'a/

sftp sd IFrro hnrrrtor)ic eSCi lla-to r

v Cx1 = \n@2xz&-- mozx-jdx : zu

Hrt)ce 1, )ttxup o,=.;, *H] ;.:1, o) L,s sort

2 (D = /(v)<r) = (v)ws Lnu,u@=+ [n rL) heufu;le_ (xr) _\ d++ J ft_llere (v) = +) oiir?:

: Ln ("r* b )fi O

ilen ce ws fr.u.J (r)= (v)E,rl I S.,\ouon

:--

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