h133_1094_5_key

h133_1094_5_key - H133: 1094 Session 5 i K61] Write your...

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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 two-minute 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 bowl-low 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“) ‘ y@,\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(E-V0)]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-.-.iamte-yo\//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 (ms-3min ) (in KNEW 15%“- m3 HP 0.?“ Emmi W cot‘ttfl’ enragtm b\\5€, has wanna one.st Ni Hams-c5 we Gob MEN‘S" iist own LwWfivcsotm minim;- (fir bumps) ‘ So keep Same-zan 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 exponential-like. 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 turnstahl.1@osu.edu 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 x-axis the energy eigenfunction (standing wave solution} corresponding to the fourth-lowest 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 fourth-lowest 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 ...
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This note was uploaded on 06/03/2011 for the course H 133 taught by Professor Furnstahl during the Spring '11 term at Ohio State.

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h133_1094_5_key - H133: 1094 Session 5 i K61] Write your...

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