Lecture_8__Raising_and_Lowering_Ops_for_the_SHO

Lecture_8__Raising_and_Lowering_Ops_for_the_SHO - v'2.+ vL....

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Unformatted text preview: v'2.+ vL. ::: ~ p (v-t it <.() (l/C'\ Vr-;t or il.1) :: C( a.i- - vJW'~ lo~l-: f\)('" S"'J~~ fh,C4r17 Co t""Il"'1rA 0\ >'01 "\ 10) -b-e;1,4S J.Q of vr;,r,I,,'~ Or~ 1. 1"''''5 C C:k< -? L-~ / l'1ut- ~/"l(/t;,.' ~}t = [,:7'/ -i~C>~ - ",= C-t LV ) (x ~ ;)C ~ 'f{X)) f J C{C?c) , ~ C:7(( P J == C ~ ~ -~t\ f G\.l.>o hul:v Cpl'''"') Is C,\6J ~ -~rO jl,,,(~ i" ~ f"rto,..7 H ex: "or q-'1: 'I O AT~ --- L G-~-~e,/-I \ _ f" c.J7C ....., - /\. - t, p J chec~ : ( - --.. +"e.J /\ ( H -Jf1;~) 11 tJr+~ -l~) a~ + So e:- e~~ ~of;;r. b.c('"Cltl-t1t:. 'Af;11J -(j) duf}... '~ 4> 1"1h"f'lv /\'. H - ('R -+ !z-J~vJ ~~ ::: 1- (H -+ ~ -t;"cJ /\ ~) H -= ~~( cQ~+ -Jz.) c aI ~ =--f H I e'";J = ~l / , ..It 'l N,~ ~ A,'f r,.J.l lI'" II "'~ [~ L~ A JH'=/1[01, , ~~ ~ c:ll"l ~~ t ~A[OIl l1 -t-Jt] t1J =twq l1j -=- .. ~ + ~ etJleV"( : n I P (VI/ 1'1,/ (J =- bv1 ("1/ Sol(/f I S Of &1J C1 We (\,. f! Jr ~~ f11 ~ -f t:-.<-v ) (b", +-t,ev] (ell 7) ~(vh'(j"") u.~ ~. .rl~~JJ ~ l;{p ~ ~ Vf pp{~J ~b (1')"/ C1Jl't<)flI'-'11~lltl1 t,. J(.l/l'lJ f/o/Jjt l:h,+ htl(r~ k'/4w ~7'1 "'.,(.",-? tliwVT S>o HI tIJ"/ -7 ? to"7/f COM""<4~ Vl .se C OtT,tf] ::- -'i!.Vq -+ -7 ~ ..f. ~W HCl~~H01i A~-t =Cf-tH ~ - O(-! K Iv'-7 VrE" I "7 V! -t "trt w Of -f ( V1 '"7 - c cV)+~w) = V1 a-f In/ --~ !fJ-rr7 Rf{,5 if(ql 7) ~ C~V) -t-cv ) (~[n/) ~ IY) ir/ :=: ~+l t17 \ (/-// Q .I1f a lV)7 :== C!J cj~ -/ ~ t}.-ttIII rr (En+-(;;w) :=h ~e-J (V7-tr~ l r1-17 .::::-C&.., -~,;) 'H In-t/ I') - --;/ --j C'c::'l ( a h 64 ~jlj r t,.r (--0 #Y\ ;, ('q , I!J ..e/\ " ~s [OW~ Y\ l-v W{,O J ~e.,J f iP) I a ~ ~ hj ( J H~("M Ylo-b teq ( ci1'Y~c.M~ t-4- YlovJ we 0\. ~ ; V~ ~ (An "..;~ 01 t;i'nft t1 S1J/V) SO ~J? I" "7 of~() J col"\)-krcf of q IS i o-t s -= (h+ 2':> isI\..q. -:> 5", -t 2"kJ _----A c?~/I V1/ 11)"7 01 ~-\, =b,,*-t:.~ oc-f In/ ~ {n-f(/ l V/::T"7 y bll1 r:. '0,,-/ :; ,,----_ b -4:..c../ :;; In -{ "/ Of OJ. (11-#1""7 =- l"1 - 2-~ r).e- t~ ~ P~rL 1p/7 COff') M J~ rq t/I/JiiL ~ {~cM""d4; <.u~.,J 1~f,J I b '1{ ~~ oJ ~y1?v O. wfb./j 01{( ~ b~ ?btu~01 ...
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This note was uploaded on 02/07/2008 for the course A&EP 362 taught by Professor Muller during the Spring '08 term at Cornell University (Engineering School).

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Lecture_8__Raising_and_Lowering_Ops_for_the_SHO - v'2.+ vL....

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