This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: H133: 1094 Session 5 i K61] Write your name and answers on this sheet and hand it in at the end.
After the indicated time, move on to the next activity, even if you are not ﬁnished! 1. Q10: The Schrodinger Equation [20 min.] In chapter Q10, we motivate the Schrodinger equation (QIO. 12). Here we consider some basic problems from
the chapter. 3. Answer twominute question Q10T.4. ‘ r
e \kae Estimv‘eh m (New? quﬁfﬁbn with m
' Og'ayoage’ﬁ‘bn {919.73. W9 0x Kw 'leﬁj E" i bowllow can we test if a given wave function psi(x) is a solution to the schrodinger equation? [See Section
Q10.4 and equation (Q10.14):] $11390 If; a solwi’icm \5; Wm NE» (3mg Hg“) ‘ [email protected],\j04)]’lipg<):g)we xi CM) 98% (5’: “in: e uoﬁm Qor‘ o“ \(oksee EQ Yr
0. Do problem Q1083 showing that b = sqrt[2m(EV0)]lhbar. [Note the him] 13 b real? ‘3}? 74am; acmbéﬁun §§§~=~Msnw M aggcrhgwk 3% «swam» new — eve) = o~ “(as (51950 is on xx? \3: igyewmo cf‘ _..Ro..iamteyo\//in J \__F d. Do problem Q1083. [Note the hint] Make sure that your answer for b is a real number when E<V0. a m can“, Men as c we
r 3 1 — 2
5C) iii—“cg; “@oy‘igﬂxi "3 W— EFVU) agax ‘: 0 °“ ‘33??? (Vt—670 ‘50 5% which W m‘ 1
) onm lo 70‘
e. Why must a physically acceptable wave function go to zero as it goes Kigalus or minus inﬁnity? 4;? mi“ N "Whyi pmbﬂoihi’ Q\CM\M gem Matan \NOU\A
\oe‘véxhiﬂc (mm g" i . loo f. What happens in SchroSolver if you choose an energy that is not an energy eigenvalue? How can you
use this to zero in on the correct eigenvalue? Try out your method. . Qn N who? his {mat (ms3min ) (in KNEW 15%“ m3 HP 0.?“ Emmi W cot‘ttﬂ’ enragtm b\\5€, has wanna one.st Ni Hamsc5 we
Gob MEN‘S" iist own LwWﬁvcsotm minim; (ﬁr bumps) ‘ So keep
Samezan cam“ Net. Kiwis mm m 3%qu menace} V: MLM\ 2. Q11: Wavefunctionology [25 minutes] Do the "Wavefunctionology Exercises" worksheet and hand it in together with this sheet. Below we give
some suggestions and hints for each part. Part 1. a. There is one error for two of the wave functions and two errors for each of the other two. b. To be systematic, consider each of possibilities B through F in turn. c. Each of the incorrect possibilities corresponds to one of the "Rules for Sketching Wavefunctions",
which are labeled 1 through 6 (see handout). B goes with rule 1, C goes with rule 6, D goes with rule 3,
E and F both go with rule 2, and G goes with rule 4 or rule 5. Part 2. First decide how many bumps there should be. Then mark where the wave function is wavelike and where it is exponentiallike.
Finally, where will the amplitude be large and small? Draw a smooth wave function with these features. Use the PhET applet "Quantum Bound States" or SchroSolver to check your answer. \\ Quin m 6mm Shake“ \fg ensue ta) EDP—F357!” Part 3. 21. Follow the same steps as in Part 2. \. ,t
b. Use the SchroSolver to check your answer. U32 ‘ MU R NF All 2‘4 n U mm S Ct h ﬁlm‘th mm ‘ n
§©$\a\ Q m l§$ w \5 Tr“. 21. Follow the same steps as in Part 2.
in. Use the SchroSolver to check your answer. Part 4. 1 eat New; “ism We as at.
———~ “‘05 03‘ N \w WC 6i W dismal criminal; H133: 1094 Session 5. Last modiﬁed: 07:55 am, April 25, 2007. \lm 9mm ‘3 WAT ‘53 \“CﬂKﬁt
[email protected] t3g m ‘ W53 with mat with an... owl mills
“will 159V a Diet tesaev.
(all 01 Why Valvt Ml “th") Nam... KEV Wavefunctionology Exercises These exercises are adapted from chapter Q11 of Tom Moore’s quantum mechanics book in
the “Six Ideas that Shaped Physics” series. 1. Each of the following potential energy graphs with energy E} marked has a wave func—
tion supposedly corresponding to the ilk—lowest possible energy. What (if anything) is
wrong with the wave function as drawn. In some cases, multiple things may be wrong;
indicate them all. You can choose from the following possible responses. The Wave function is. . . A. correctly drawn (more or less). B. incorrect because it curves toward the axis in a forbidden region or it curves away from the axis in an allowed region. C. incorrect because its wavy part doesn’t have the correct number of bumps (or you
could count nodes instead). incorrect because the amplitude of its wavy part is wrong.
incorrect because the wavelength of its wavy part is wrong. incorrect because one of the exponential tails is the wrong length. 9.1.91.5 incorrect for other reasons (specify). 2. Sketch on the xaxis the energy eigenfunction (standing wave solution} corresponding to the fourthlowest bound state energi for a particle whose potential ener is shown by the graph below. ELF") ll NW5  $1M P‘Mﬁ 0 i0‘ \ Wt W‘m 0“!
. “that 113% class? to i a. energy 3. Sketch on the 32~axis the energy eigenfunction (standing wave so]ntion) corresponding to the ﬁfth—lowest bound state energy for a particle whose potential energy is shown b the ra hbelow. E \ﬁU‘ S'I‘E‘C— ‘ N \Nﬁxkl E y g penergy 5 NW3 . ﬁbﬁmﬁgom MJ 0“ is; M (n might. 4. Sketch on the x—axis the energy eigenfunction (standing wave solution) corresponding to the fourthlowest bound state energy for a pérticle w ose potential enesfg)‘ is shown
by the graph below. E“\ 90 Ll W5 'ﬂﬂblﬂ ﬁlms “\ i0‘ 155% a b \ L\l3?. A D]
  . .. A ' 1 NJ energy. . . ' . M w? m mail “Mil ...
View
Full Document
 Spring '11
 Furnstahl
 Quantum Physics

Click to edit the document details