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CHEM113A P_08_soln_113A_W10

CHEM113A P_08_soln_113A_W10 - f Preview#08(Chem113A W'10...

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Unformatted text preview: f Preview #08 (Chem113A W'10. due Wed. 01I20i'10 at 12:05pm in class) Assigned reading: Engél 3.3--3.5 (ver. 1) Attendance record: I am M present at or[ ] absent from this class meeting (see date and time above). Name: Eng :ii [[1 WW“ HMS Forming study groups is permissible. but you must construct your solutions independently. By writing down my name, i confirm that l strictly obey the academic ethic code when doing this preview and my statement on attendance (above) is correct. Please write down the names of everyone who you worked with on this preview in the space above. [1] Result of individual measurement. When one measures the energy of an electron in a 1D box of length 1nm in an unknown state, what are the possible observed values? (Hint: Postulate 3. You may find Engel 4.1 (ver. 1) "Particle in a 1D Box" helpful.) — “241% + \I(><)\P(><):E‘P(x) ,00 V70 2m ciX" - ,? V109 O E \i)"0 \Aflslrdgboxfl EWCX): “ha Mili V("<’):‘O 2m 0W” 0W 0* fiEh’ hint {3le airilflm —%i mewmmn:ci.ii¥i0 iC0\ i4; Mamie“ ‘mli‘Cfi/g En: (swamped mqu‘ a “2 S [2] Expectation value. Denote the eigenfunctions of the Hamiltonian operator H for an electron in a 10 box of length 1nm by ¢n(x) (n=1,2,3...). Now this electron is in a superposition of states, described by the wavefunction l-l"(x) = 112*¢1(x) + sqrt(3)12*¢2(x). if one measures the energy of this electron, (i) what are the possible outcomes (numerical values) and corresponding probabilities (numerical values)? (ii) what is the expectation value (numerical value)? (Hint: Postulate 4. Again, You may find Engei 4.1 (ver. 1) “Particle in a 1D Box" helpful.) v 1mm 10K. . / [l] €\039«v'1fwrm\'omf43mm %V_..‘fl:‘\2\31"' KP(><)= 1100+ 123%) 0) 170351019 ém'CM whom? 1 fi]‘( {1:}, E : i \ | LFOV WA. Mm MW in #1 mexoawm‘es of 201131 swig ' {WSW 1, Pfh‘é "’> Pf tr . Far fi’dtfiZl P:(%)z_’ {13—2— GQQE‘XWHW‘IDr V1110, W I <51): — w ’0‘de :"2\\0m\20\m I” ; Preview #08 (Chem113A W’10, due Wed. 01IZDI1O at 12:05pm in class) Assi ned readin : En el 3.3--3.5 ver. 1 Attendance record: I am M] present at or[ ] absent from this class meeting (see date and time above). Name: Qarrl‘lfll'a. 5W3 Forming study groups is permissible. but you must construct your solutions independe 1y. By writing down my name, I confirm that I strictly obey the academic ethic code when doing this preview and my statement on attendance (above) is correct. Please write down the names of everyone who you worked with on this preview in the space above. [1} Result of individual measurement. When one measures the energy of an electron in a 1D box of length 1nm in an unknown state, what are the possible observed values? (Hint: Postulate 3. You may find Engel 4.1 (ver. 1) “Particle in a 10 Box” helpful.) ~ Tl? a? . .e ,4— ' e’fi- "‘—"_ "J V V Total (mail? OFTITI of . 9m (13),; ( ) POfiuato 3; m am) glflgluo Wyfg'sgycrrrm-r Op ‘H/lQ ObSC-W‘Jd/bi? +fl0+ (4‘ \J a" ‘ y r' COH‘fspor‘ds +0 439"; apt-army ,A _J #3 ant; galyeg am a-r LMll QM)“ be W"95134W°{ 9-1": 4M eigenvalues 0P +1:er op-ml-D‘r. Tl 2 2 F ' r - o s a , - m ,9,”— + nix) Is (Ln apC/malsfl’ "'W “71-1" ”5’90 ”NJ”? ‘“ 2m 9x2 ”‘ 1 tron Wanna! arm/m l5 _.055m.9, no forms (“an be admj' 0” Am elec so it? (cinsramr and l'nctrponcfiur'r a? y and ‘t- it): 414)”) + UPGK‘H’} '—“ 11*”) lm (fly; ”Mum VU) IS (Diagram, (am MODS-C *9 ”Wat 3+ Z’W Wrongs fish; a; no turd Marmot. Fol'n'f {or m 2210 of VU) 2 x Q. _ w. L 1.. dx2 "i1 [2] Expectation value. Denote the eigenfunctions of the Hamiltonian operator H for an electron in a 1D box of length 1nm by ¢n(x) (n=1,2,3...). Now this electron is in a superposition of states, described by the wavefunction llJ(x) = 112*¢1(x) + sqrt(3)l2*¢2(x). If one measures the energy of this electron. (i) what are the possible outcomes (numerical values) and corresponding probabilities (numerical values)? (ii) what is the expectation value (numerical value)? (Hint: Postulate 4. Again. You may find Engel 4.1 (ver. 1) "Particle in a 1D Box" helpful.) ———————————— _ Efl_d~b»<aflfih / {k}?! (5 f 2 o _ __l L — P — firm-"2 “I D? :- ‘ H V7777%77774777#'“m'—- I m - ——_- Ha; 712;:3f5;;;;‘_ -- -- L] I‘ _.___ ——-——--———k-T l) m, H $3-.ng , Ly 9.1-ng r. _w _Mim i _ Agii grfi .A__. _ ,47;777w~_...._m.._.._._.. _ A ifi ._... _— , .__ 3—._ 2.”, fififi _. “_u ifi _J .. ._Hjuwifag m as Qrcuowa m'kuw : ' F a i ,M.____ m 7”,, ,. ,r.l?_..._'{._.. M‘ ,7 _ZIYT .g§;, .u A , WT _ ( 7H)!“ ______ __ , , * 4’3”“ _.. 924x; 53 Wigs) —— ~~ — fir ___ ’ A229," ___.imax__ 1 3‘ ifix W k , _ . 2 x . —‘ — “it Wm Edit?) — } ’316P1‘{‘3‘J"“" "£3" Efficbi-H} , ~~ - - ~7 A , ; 2x: Dmi'jxi ‘ ,9 ax M n__ ,V,‘._,.____.__,,_CXSSML£ QMXQWMVWJS+W4 “EX/1).u.__ _m.‘ fif _-. ____ ,2?” _“__ £1);...;'..v:“,::" 51 ‘ m h __ ‘ WV f _W- k = j L ‘A ' L W L j ’ ' " ‘ V“‘"“"—— $I;}—'—Ifi: '“ “‘ C‘éii'; Trxn- \ R7 — _k a — 7W ,._ .___.__ .__‘A_L:u9ffi~ V, ._.-.- _I;__ _.._._,_‘_,.A,, E.__/_\L_ _:_.._ 7 - 7 " _.__._- (727,777,. __ __ , .___‘_____.___ ._,. . ,, _ _. 7 7 __ m __ -_w 5:32:51; ‘ 1 _SIIL IE5 \I’: "‘2 9y 3 L ‘ ‘L—__ "Ta—j 7 fl 7 —— M 7 _— V _ _r 7""\."""' __ _ " "7 W ' «jflT—‘_'7—“Wfi‘\ _— _ 7’ '— __ ———1 ”a? _..._—_ ~ bkiww _t_._)& ”ELM—Lu” ._ _... ._.‘_,_fi7 , _ _— __ :7, 3.9:”. L ...
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