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# quiz7solutions - Page 2 of 2 Problem 1 Drawing Lesson I |12...

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Unformatted text preview: Page 2 of 2 Problem 1 : Drawing Lesson I |12 ptsl : Consider a particle moving in a one-dimensional box with rigid walls (U=oo) at x: —Lf4 and x=L/4. (a) Sketch the potential in all regions of x , (1)) write the wave functions and probability densities for the states n=1, 2, 3 (c ) sketch the wave function and the probability density in all regions of x, ((1) Calculate the ground state (n=l) energy of the particle. Problem 2: Not Ilust Another Brick in the Wall ! I8 Qtsl: Suppose that a particle of mass In is trapped in a potential well that has rigid wall at x = 0 (U = 00 for x < 0) and "a finite wall of height U=Uo at x = L. See figure below and assume particle energy E < U0. (a) Cleanly sketch the wave function for the lowest three states and be sure to label points x=0 & x=L on your sketches, (b) What is the mathematical form of the wave function in the ground state in the three regions x < 0, O < x < L and X > L ‘2 a \\ a a a §\\‘\ i S \s R (ﬁll 4| 4 gases 5%??? IIIIIJ eaten a: \\\\ ‘5‘ est \S‘b‘SSS't‘ an: «A \$& win“ \$ «5w. §s§u § ‘- «we at § 1; \ 3' 7 UV 'VV'V'V". V. F... eaeeeteeea emeeeeeee 5333\533533538’Ih‘b‘b Rk’s‘ﬁ’ﬂﬁﬁﬁﬁkﬁ assessments '5 \\\‘§\& \ S a \\\\\\\\ \ are: « §§§s V 5 a s s wit“ & (b) waudlunchm haw vcmsk £0» X>L :[Q . A ““CL ’“ "VJ-1 Jami ﬂu, wm-Qumc-hm LL=0 mug-k o\€o be cmﬁ—mugu; cwbwhra 350 %(+L/q) : VI(-L/L[) :0 Hue Schrb'clwﬁur's 81)“: 1 1. -Eé Y’ 4'“? 2': Era 2'“de man. :4... watt ) um I -5 ill? =EYI 2M AK 41 2 'L ..._ : "' E —_ -: 2 E ‘5sz“ %1%,k%jk 9&1. an). “an So‘u-ﬁrtms 40 {in atw'amMAo-Q/ '31“: 6‘0 'hx): Asm [KX hf; ) + ‘Bcos [um +95) “V5 m9°56 “‘0 CMWWM P('L/L1)=Y’(+L/H>: 0 2"(‘L/4): ham, (”qu- +é) +3028 (—11%;- Jrsé) =0 lei-‘9 choose) if: +kL 1 M Ll +L-L/L‘) : l3; gm {43. Fur) +3 CM (43;. +k’L.) ‘1 L: H L1 3 0 9““! Sm“) 1" J 035(6) : L we. have, 3:6 ﬂow fléi'L/LO: : A sum (Kl- +L(\_ :- A 5‘“. C ML. 1 ‘E'OC 9m +0 Venn ‘4‘» quc Muq+ haue. L. K... : m1- => K: 2M:- 2' L. ( you. Cou‘dv home also annual, 03’ LX‘L/Li) 369mm?) u‘mm “Hrw ordn- mz when tame impose-d, ‘H‘Ub bounclofa Cbﬂdxlt—Lm5) Na...) \el—‘s QmA, Hm nofNU-nga-Hm mam): "7’4 P32 3 dx s.nz[7-.“_‘."(K #101: l -L/ '- L, 19+ U»: 2.1“ (X+L/L1> L horn-lg than?) *0 d)“. : Znn- clx MY. ‘2 S S° dIK: .3; All; 0 1mm” m1, 2‘ ﬂﬂ' 1 2- \ \ LA (in cmu, ~LPx Kim -'—5m2.u. EW 0 {If H a 2. 3 LR :\ \$m (A13) ‘SunACOSB 1'. COSASH‘IE =5 Wt): ‘1 s.“ 2m“ + '11“ n L ‘1"- 2- 7th:) :J—i 5'“ (.211?) “,5an -I- cos (2'an 5m cm' " L- ‘- 1 “E. "7". {Ear n=\ ’7‘) :' 1 COS 257%. I L. '1': ﬁzz, E’Li): i 5‘“. Ll‘ﬁ‘)‘ (iorac’f «\aou’r (“5|“ka > L. I 913'“ h: 3 7’3 (X) 3 d5- C 05 013C ( 41°"? aback ﬁlms can ) L L mama 4h. thhab«\\’fadmsl*|€9 ore; {Jug-V ”all “=1 )6‘ \Y‘H-L I I l "“ —“ *—“ " (cl) “Wu: and?!» o'? M) -L KB L l V6113 1; so a T1 \ “M [M anus-an; 7. jusar +1 w .___...__ x a: “a? \ Zm (1;): 1 z ”"3 (“L-L 7L. 3 15%? I m x s (‘5') ﬁx) = 0 ﬁve. muohncﬁﬂm Musi' unmgh ‘n Pea-cm. (11) {I} (3537-) 5mm 44L” poWaQJ 15 Ingmd-o NFC/J So - LL=O we ms-Vr ca-hsﬁa 'Huu CMC‘AHN/ 'ILH-‘Ozo \$u Hm WaMunc¥Lm "HI be Cm*~““°u5. m mam (It) . Sckr‘édmapr"; Cdbﬂ mac}; (0(X4L) -4k1 J2 P : Etf’ siﬁ‘c’ U30 hC‘FCJ 1 dx‘ 1;?— (1“) =7 yum: Asun. (Kx +9!) 4454335 (M +90 impose, conA1+th 5L(E)<°) :6 =7 ?L[¢)(o): Asunff +Bcas/4{ :6 choose. 76:6 lam-i Lac, ab‘Hun. 5:0 L201.) -+’~d_zzoab+u¥l= E)“ ,Wuo max {11% = 2m LUKE) )4 dx 3?; «out. :Luo so ZMWO E) >0 \ S (III) “K ‘KX 'Hw‘s. h09 50hr» (M '2‘]th :' A8 Jr Re b‘k‘. 05 Kw.) w e ""> CO ? S‘o uJC, 6245' R50 ’ Stnq/ 4kg, mauLRanMm Mug-P be; 4-“an swan-3M3}. (m2) 27‘? (x) 1' 156°“ 50 {My mowcunc'K-GG‘MS and; MO P‘m‘ba‘mh‘ﬁé dW5l¥|e\$ ‘ODK ‘\K6 7. \ Af ﬁmndsh'ro AH I you 3"3 no‘r I ‘ bade} ”LO ; ‘1 skesrch “of" 7. 4 O I_ 5 x < O L )C V V £51;- em: “-CA iM‘O ...
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