(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 66821, 2914]*) (*NotebookOutlinePosition[ 67527, 2938]*) (* CellTagsIndexPosition[ 67483, 2934]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Visualizing Particle-in-a-Box Wavefunctions ", "Title", TextAlignment->Center], Cell["\<\ By Edmund L. Tisko Department of Chemistry University of Nebraska at Omaha Omaha, NE 68182 etisko@unomaha.edu Translated and modified from the MathCAD document by Alex Grushow 2004\ \>", \ "Text", TextAlignment->Center], Cell["\<\ \[Copyright] Copyright 2003, 2005 by the Division of Chemical \ Education, Inc., American Chemical Society. All rights reserved. For \ classroom use by teachers, one copy per student in the class may be made free \ of charge. Write to JCE Online, jceonline@chem.wisc.edu, for permission to \ place a document, free of charge, on a class Intranet. \ \>", "Text"], Cell[CellGroupData[{ Cell["Laboratory Procedure", "Subsection"], Cell[CellGroupData[{ Cell["General instructions for obtaining energies", "Subsubsection"], Cell[TextData[{ "Read each section to learn what kind of potential function, V[x], your box \ has.\n\nDecide what kind of boundary conditions you expect your wave function \ to satisfy in order for it to be considered ", StyleBox["well-behaved", FontSlant->"Italic"], ".\n\nEvaluate ", StyleBox["every", FontSlant->"Italic"], " input cell by clicking in the cell and pressing Shift-Enter (generally, \ there are either one or two input cells to evaluate. 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.29489 .05618 L .29509 .05618 L .2952 .05618 L .29531 .05618 L .29549 .05618 L .29569 .05618 L .29589 .05618 L .296 .05618 L .2961 .05618 L .29629 .05618 L .29649 .05618 L .29667 .05618 L .29684 .05618 L .29702 .05618 L .29722 .05618 L .29742 .05618 L .29753 .05618 L .29763 .05618 L .29785 .05618 L .29796 .05618 L .29807 .05618 L .29826 .05618 L .29847 .05618 L .29867 .05618 L .29885 .05618 L .29902 .05618 L .29921 .05618 L .29938 .05618 L .29954 .05618 L .29972 .05618 L .29992 .05618 L .30011 .05618 L .30029 .05618 L .30049 .05618 L .30067 .05618 L .30084 .05618 L .30102 .05618 L .30122 .05618 L .30143 .05618 L .30161 .05618 L .30181 .05618 L .30202 .05618 L .30221 .05618 L .30231 .05618 L .30242 .05618 L .30254 .05618 L .30265 .05618 L Mistroke .30285 .05618 L .30304 .05618 L .30324 .05618 L .30345 .05618 L .30363 .05618 L .30382 .05618 L .304 .05618 L .30417 .05618 L .30436 .05618 L .30457 .05618 L .30477 .05618 L .30495 .05618 L .30515 .05618 L .30535 .05618 L .30555 .05618 L .30573 .05618 L .30594 .05618 L .30606 .05618 L .30617 .05618 L .30637 .05618 L .30649 .05618 L .30659 .05618 L .3067 .05618 L .30681 .05618 L .30702 .05618 L .30713 .05618 L .30724 .05618 L .30736 .05618 L .30748 .05618 L .30759 .05618 L .30771 .05618 L .30782 .05618 L .30792 .05618 L .30811 .05618 L .30832 .05618 L .30851 .05618 L .30873 .05618 L .30893 .05618 L .30911 .05618 L .3093 .05618 L .30946 .05618 L .30965 .05618 L .30984 .05618 L .31003 .05618 L .31024 .05618 L .31042 .05618 L .31062 .05618 L .31083 .05618 L .31095 .05618 L .31106 .05618 L Mistroke .31127 .05618 L .31147 .05618 L .31164 .05618 L .31182 .05618 L .31202 .05618 L .3122 .05618 L .31237 .05618 L .31253 .05618 L .3127 .05618 L .31288 .05618 L .31306 .05618 L .31326 .05618 L .31344 .05618 L .31361 .05618 L .31381 .05618 L .31392 .05618 L .31402 .05618 L .31421 .05618 L .31441 .05618 L .31461 .05618 L .31482 .05618 L .31502 .05618 L .31521 .05618 L .31539 .05618 L .31556 .05618 L .31575 .05618 L .31593 .05618 L .31613 .05618 L .31634 .05618 L .31652 .05618 L .31672 .05618 L .31693 .05618 L .31705 .05618 L .31716 .05618 L .31737 .05618 L .31757 .05618 L .31773 .05618 L .31792 .05618 L .31812 .05618 L .3183 .05618 L .31847 .05618 L .31863 .05618 L .3188 .05618 L .31898 .05618 L .31916 .05618 L .31936 .05618 L .31954 .05618 L .31971 .05618 L .31991 .05618 L .32002 .05618 L Mistroke .32013 .05618 L .32031 .05618 L .32051 .05618 L .32071 .05618 L .32082 .05618 L .32092 .05618 L .32111 .05618 L .32131 .05618 L .32149 .05618 L .32166 .05618 L .32184 .05618 L .32204 .05618 L .32224 .05618 L .32235 .05618 L .32245 .05618 L .32266 .05618 L .32278 .05618 L .32289 .05618 L .32308 .05618 L .32329 .05618 L .32349 .05618 L .32367 .05618 L .32384 .05618 L .32402 .05618 L .3242 .05618 L .32435 .05618 L .32454 .05618 L .32474 .05618 L .32493 .05618 L .32511 .05618 L .3253 .05618 L .32549 .05618 L .32566 .05618 L .32584 .05618 L .32604 .05618 L .32625 .05618 L .32643 .05618 L .32662 .05618 L .32683 .05618 L .32703 .05618 L .32713 .05618 L .32724 .05618 L .32736 .05618 L .32747 .05618 L .32767 .05618 L .32785 .05618 L .32806 .05618 L .32827 .05618 L .32845 .05618 L .32864 .05618 L Mistroke .32882 .05618 L .32898 .05618 L .32918 .05618 L .32939 .05618 L .32959 .05618 L .32977 .05618 L .32996 .05618 L .33017 .05618 L .33037 .05618 L .33055 .05618 L .33076 .05618 L .33088 .05618 L .33099 .05618 L .33119 .05618 L .3313 .05618 L .3314 .05618 L .33151 .05618 L .33163 .05618 L .33183 .05618 L .33195 .05618 L .33206 .05618 L .33217 .05618 L .3323 .05618 L .33241 .05618 L .33252 .05618 L .33263 .05618 L .33274 .05618 L .33293 .05618 L .33314 .05618 L .33333 .05618 L .33354 .05618 L .33374 .05618 L .33393 .05618 L .33411 .05618 L .33428 .05618 L .33447 .05618 L .33465 .05618 L .33485 .05618 L .33506 .05618 L .33524 .05618 L .33543 .05618 L .33565 .05618 L .33576 .05618 L .33587 .05618 L .33608 .05618 L .33628 .05618 L .33645 .05618 L .33664 .05618 L .33683 .05618 L .33701 .05618 L Mistroke .33718 .05618 L .33734 .05618 L .33751 .05618 L .33769 .05618 L .33788 .05618 L .33807 .05618 L .33826 .05618 L .33843 .05618 L .33862 .05618 L .33874 .05618 L .33884 .05618 L .33903 .05618 L .33923 .05618 L .33942 .05618 L .33963 .05618 L .33984 .05618 L .34002 .05618 L .34021 .05618 L .34037 .05618 L .34056 .05618 L .34075 .05618 L .34094 .05618 L .34115 .05618 L .34133 .05618 L .34153 .05618 L .34174 .05618 L .34186 .05618 L .34197 .05618 L .34218 .05618 L .34238 .05618 L .34255 .05618 L .34273 .05618 L .34293 .05618 L .34311 .05618 L .34328 .05618 L .34344 .05618 L .34361 .05618 L .34379 .05618 L .34398 .05618 L .34417 .05618 L .34436 .05618 L .34453 .05618 L .34472 .05618 L .34483 .05618 L .34494 .05618 L .34513 .05618 L .34533 .05618 L .34552 .05618 L .34574 .05618 L .34594 .05618 L Mistroke .34612 .05618 L .34631 .05618 L .34647 .05618 L .34667 .05618 L .34685 .05618 L .34705 .05618 L .34726 .05618 L .34744 .05618 L .34764 .05618 L .34785 .05618 L .34797 .05618 L .34807 .05618 L .34828 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.05618 L Mistroke .38069 .05618 L .38087 .05618 L .38107 .05618 L .38125 .05618 L .38142 .05618 L .3816 .05618 L .3818 .05618 L .38201 .05618 L .38219 .05618 L .38239 .05618 L .3826 .05618 L .38279 .05618 L .38289 .05618 L .38301 .05618 L .38312 .05618 L .38323 .05618 L .38343 .05618 L .38362 .05618 L .38382 .05618 L .38403 .05618 L .38421 .05618 L .38441 .05618 L .38459 .05618 L .38475 .05618 L .38494 .05618 L .38515 .05618 L .38535 .05618 L .38553 .05618 L .38573 .05618 L .38594 .05618 L .38613 .05618 L .38631 .05618 L .38652 .05618 L .38664 .05618 L .38675 .05618 L .38696 .05618 L .38706 .05618 L .38717 .05618 L .38728 .05618 L .3874 .05618 L .3876 .05618 L .38772 .05618 L .38782 .05618 L .38794 .05618 L .38806 .05618 L .38817 .05618 L .38829 .05618 L .3884 .05618 L .3885 .05618 L .3887 .05618 L Mistroke .3889 .05618 L .3891 .05618 L .38931 .05618 L .38951 .05618 L .3897 .05618 L .38988 .05618 L .39005 .05618 L .39024 .05618 L .39042 .05618 L .39062 .05618 L .39083 .05618 L .39101 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.05618 L .41277 .05618 L .41289 .05618 L .413 .05618 L .41312 .05618 L .41323 .05618 L .41333 .05618 L .41352 .05618 L .41373 .05618 L .41392 .05618 L .41414 .05618 L .41434 .05618 L .41452 .05618 L .41471 .05618 L Mistroke .41487 .05618 L .41506 .05618 L .41525 .05618 L .41544 .05618 L .41565 .05618 L .41583 .05618 L .41603 .05618 L .41624 .05618 L .41636 .05618 L .41647 .05618 L .41668 .05618 L .41688 .05618 L .41705 .05618 L .41723 .05618 L .41743 .05618 L .41761 .05618 L .41778 .05618 L .41794 .05618 L .41811 .05618 L .41829 .05618 L .41847 .05618 L .41867 .05618 L .41885 .05618 L .41902 .05618 L .41922 .05618 L .41933 .05618 L .41943 .05618 L .41962 .05618 L .41982 .05618 L .42002 .05618 L .42023 .05618 L .42043 .05618 L .42062 .05618 L .4208 .05618 L .42097 .05618 L .42116 .05618 L .42134 .05618 L .42154 .05618 L .42175 .05618 L .42193 .05618 L .42213 .05618 L .42234 .05618 L .42246 .05618 L .42257 .05618 L .42278 .05618 L .42298 .05618 L .42315 .05618 L .42333 .05618 L .42353 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\[CapitalPsi][ 0] \[Equal] 0, \(\[CapitalPsi]'\)[0] \[Equal] 0.1}, \[CapitalPsi], {x, 0, 4}, Method \[Rule] ExplicitRungeKutta, MaxSteps \[Rule] 800];\)\), "\[IndentingNewLine]", \(\(\(Plot[\[CapitalPsi][x] /. \[InvisibleSpace]solution, {x, 0, 4}];\)\(\[IndentingNewLine]\) \)\), "\[IndentingNewLine]", \(Print["\< At \[CapitalPsi](L)=\>", \[CapitalPsi][ 4] /. \[InvisibleSpace]solution]\)}], "Input"], Cell[TextData[{ "Assignments:\n\n1. Find all of the states for which the energy is less \ than the step potential (V=20).\n2. Where is the particle most likely to be \ when it is described by these states?\n3. What relationship is there between \ energy and the degree of barrier penetration?\n4. What relationship is there \ between energy and the rate of decay inside the barrier region?\n\n5. Find at \ least two states for which the energy is ", StyleBox["greater", FontSlant->"Italic"], " than the step potential, but E < 30.\n6. How does the particle's ", StyleBox["wave length", FontSlant->"Italic"], " vary across the box?\n7. What does this imply about: 1) the particle's \ velocity in each region, and 2) the probability of finding the particle in \ each region?\n8. You should notice that when the particle's energy is just \ slightly greater than V, the particle has a much higher probability of being \ in the step region, but when the particle's energy is much greater than V, \ the particle spends roughly comparable time in the two regions. Why?" }], "Text"] }, Open ]] }, Open ]] }, Open ]] }, FrontEndVersion->"5.2 for Microsoft Windows", ScreenRectangle->{{0, 1280}, {0, 951}}, WindowSize->{832, 628}, WindowMargins->{{10, Automatic}, {Automatic, 0}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic} ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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