preview + h.w.1

preview + h.w.1 - Preview#05(Chem 113A W’07 due Fri...

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Unformatted text preview: Preview #05 (Chem 113A W’07, due Fri. 01I19I07 at 11:05am in class) Assigned reading: Engel 2.3——2.5 l ,Attendance: By writing down my name, l confirm that I was physically present during the entire lecture. Name: x [Q5221 0332 i/ 7’ Academic ethics need to be strictly obeyed. Forming study groups is permissible, but you must construct your solutions independently. Please write down the names of everyone who you worked with on this preview under your name. Back: private communication (optional: any questions, comments, learning difficulties, etc., that you want to tell me or the TAs privately) [1] Complex functions. Quantum wavefunctions are complex in general. Problem P2.8 (scanned below for your convenience) is a simple exercise on complex functions I P23 Express the following compiex numbers in the form (1 +112, & Zeifigz C em 3?): . b 2638"“: d .. F6)?“ D+-13 " h \T\ /l ,2. Q \ - \ <7 ) <2 ' “T / a” a; (ass—w I t. f( i"1 4' 512/1 F I A a l\ ». E \ 7?“ “(f/r (\U 31‘ b) x .5 x 77".“ *‘ >,, A :r ‘P\ 1’ a: 1/, )L ‘ 3". A ‘ 7 ‘1’ \\ m {a ’ 1; + Isl PAL.) : 2 ‘7} { “\U ~ ,P r K »~ .,.,;~ ( ‘i, r; l ) \ ~ “.5 ~ 7’ “ r 235 \ x“i\. L : 'Z i f o" A M g ’t l j 2.“: ‘7' a .2 r / 3. / r f t x y 1:} _;;s .47 W 1+) } I: "’— r; 34 . s 3%; 3. “at § [2] Eigenvalue problem. Solving eigenvalue problem is one of the most important math skills in QM. Problems P2.11 (scanned below for your convenience) /’P2.1 1 Determine in each of the following cases if the function in the first column is an eigenfunction of the operator in the second comma. if so, what is the eigenvalue? [1/ f g , A . M f i'\ (W a. x3 dis/{Ix3 /\ b, x y x(6ffix)+ flit/5,3“) B 0 Meow 63.1862 ' ——-—->(, 2 MIL)? 3t¢"’”"""/I [IML/ 4's YQchVQ . «*5 ‘ : z “5‘ (>2- 6ixr’o"3g“’i"*‘"’“j is 5’00“!on MEX/o'jflonrm’j a 3 52mm? «/ 2: )7 < : 3 k» {Cox/MG}, 7-} A; é H5 «:03 M /g / g A C f L J K ' ICC’X/L as o/“~ L {V / ‘5. 0'I’Yél'vr!w)~/“noé X/0 “74/ A 2 [’9 I :, “‘Ms 7*" 7-{OX/‘3yk (Dirt/$1 “ :fi) 07 .-=”“E.L:“L"§ 3 'w t a I , .{I vii“ wk"! :7 1 V f X L N/ >( 'fki ir> A‘nhfl X444 r: .( ’w—v—w— {_ ehv/m 1 Let jaw/m : K :) Er E g ‘l g \ :7 RE SMMEKA my”; E 1-; : X!0”3‘!r1,3 x Lhdo'ggrf V Qrk A“ /“ \ 5.1129 >05 WW5 3‘ ero‘zs" 6 Ixaxo‘H/o‘lig/IZ 606‘: k ~ l ’3: g. 15 x/WQE E h V )4 Ct.» : x15“ m m w .33 i afijw ‘ “11 “I hv/k."q M KT : thW/uflo 3/; Xér-m 34 ct: “, fl g~ 2 gX/C‘JJ by _ 6.6) 6H'o'qu )HQQ E: Tc X C I A “Le” (4 .M i >e‘~\ ‘ X \ «:7 {2g AWC‘Q‘ L2. (20394 55551xyo"3‘*].2 X 4300') g" “‘- ‘ Alpblxhiwé's" 4:06.25" d e “3397*”‘233/2‘ 60m: 14 “ l c1: 8. I§ x/D‘JK;i E W % qfi' 1' 1% ~— .~ ~— ~313- / 3. 935ij Max/1415’ hV/kwi w (<7 : Itifiu/gfo Xgflwcgé g. 2 XX/QW)U ~\ Er RE: t _"’P'” g.—0.0/62 / L“ ’T '1 2.000 ‘ § .JLL‘ amémwhuyxg‘? E‘ ehk’-\ - aéuro‘wfufnv’“ e, LgYONu-T'ngmck a! C: Q 65 X lo'mj ‘. maul ’E‘ . .‘ a my (0 Weak {11 (r a. 2 £72 /.+ >4 JVJ-.XLJ< fly. \ X OgC , x0 y : Q /+ 6 Own) # [exfxvnj 2' X K T'geH-wj : 63+ 8% T fie’yz -* I + y Ell/K Q€ g 4 «:-;.y§1 B :‘ Irv "M ‘1 Jar /§x H7<€ fixe +516 .4 E " A Y A 00* .y’ I" fl f r» N— 0§C Mu... 2 7/ 7’6 "x fix ._ / C7564) ~ A :37 5». f", Xngt COSC /K)~/-)</U~I’f x)” 0.037 2 /‘ $00k '. \ AV w )7 ‘x’ Law/15W“? , ‘77"? * M * 00760( xguvk ; 1’) X /‘ Qo/rc":M b£)3 ( v ‘1 ""650 I I : C) ( autiéu¥ ELEV)" 4&00955?) V k V ' .7 i DNA/37 ,fm‘ {m3 yea/Lynn fie/ween V ~th/6‘fcfl a [if 7 W712: I OH YD/Uv»~n / Wm» M “ti/91"“ :- SWV‘ 1: L ; )(Logc)i’ C. E054 : :|)fi;) IXL‘M» cl: 5 4.3 “yd/0;] / k) / v PU) (7K Q 7" P.”~§——.—I;- UC’E:MV g6, “A? A - nhv/ ~37; L :7 i 17:, : “e a?) 8”” ’l/fl'f 2 UK!” L? V5 W MW ., -‘....,_..- -W'm' ’- f E? .. (é / f QWAVB I [15/ K a) “7 6’7 (/0 {711' L: M m [M .533}, /9 $2.34“ :u/s‘é/ 35 cM/ m0h4¥om~Y /—/o 5/2 1L P7653411,“ m ‘70 3/5 (CM, ‘ [Wm—2m v! if ,t ngx MM; P0314- OW ‘« CA {F’tlp€h(/ €54 ‘a (j {Aug 031* Q fill?) KW, £5 mam MW“ f glow/2.67 (f / ML [65% 73 ’r’fiflfl/ / (3/! 5/7/91 «2 Y, alias» /’/0La€;/Fr , .Cxlerr-z'WM’S 7(6)”! u/uey. IQ? ~ “2": If” baffle; rm —-/0-' 2”» Lanai/3’2.“ [’2 war! y , f/(z mgr/W . I L'fla’f,»ec,/ / n fl? 75 AM, VA (j: “[611 . [I {31% g ff £5) a : CV : <37 " 5(3M Eorc.)) ‘ w ~t/ ’7 AV l e y/mvl :[9 ( 3M? 37 0 KM” UP 6J0 7 )] (firings Is. .50 Erna/I 1/ lbw/flag. fl-fleu .43 Hgf fioWCEflML. I . may +0 4: 8209A; rte/543m, WWW it; (logo I r . AS “’3- CW‘ $21.. , y I'TS So gonad chLe {A}. 19/4“! PM!” :3 rnfi POSséifit M fibnflvf L/ («76, T14 Mflin finger: I: - .,.2 “433 t; {Lat LU "21 L03 a , mo“) mix-(k. arm-1L2; a; ‘}\ ethane? swag”. ...
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