(************** 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[ 82482, 3860]*) (*NotebookOutlinePosition[ 83188, 3884]*) (* CellTagsIndexPosition[ 83144, 3880]*) (*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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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 .05618 L .34848 .05618 L .34865 .05618 L .34884 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.05618 L .35975 .05618 L .35992 .05618 L .36011 .05618 L .36032 .05618 L .36052 .05618 L .3607 .05618 L .36089 .05618 L .3611 .05618 L .3613 .05618 L .36148 .05618 L .36169 .05618 L .36181 .05618 L .36192 .05618 L .36212 .05618 L .36222 .05618 L .36234 .05618 L .36245 .05618 L .36256 .05618 L .36277 .05618 L .36288 .05618 L .36299 .05618 L .36311 .05618 L Mistroke .36323 .05618 L .36334 .05618 L .36346 .05618 L .36357 .05618 L .36367 .05618 L .36386 .05618 L .36407 .05618 L .36426 .05618 L .36448 .05618 L .36468 .05618 L .36486 .05618 L .36505 .05618 L .36521 .05618 L .36541 .05618 L .36559 .05618 L .36579 .05618 L .366 .05618 L .36617 .05618 L .36637 .05618 L .36658 .05618 L .3667 .05618 L .36681 .05618 L .36702 .05618 L .36722 .05618 L .36739 .05618 L .36757 .05618 L .36777 .05618 L .36795 .05618 L .36812 .05618 L .36828 .05618 L .36845 .05618 L .36863 .05618 L .36882 .05618 L .36901 .05618 L .3692 .05618 L .36936 .05618 L .36956 .05618 L .36967 .05618 L .36978 .05618 L .36997 .05618 L .37017 .05618 L .37036 .05618 L .37058 .05618 L .37078 .05618 L .37096 .05618 L .37115 .05618 L .37131 .05618 L .37151 .05618 L .37169 .05618 L .37189 .05618 L Mistroke .3721 .05618 L .37228 .05618 L .37247 .05618 L .37269 .05618 L .3728 .05618 L .37291 .05618 L .37312 .05618 L .37332 .05618 L .37349 .05618 L .37368 .05618 L .37387 .05618 L .37406 .05618 L .37423 .05618 L .37438 .05618 L .37457 .05618 L .37474 .05618 L .37492 .05618 L .37512 .05618 L .3753 .05618 L .37547 .05618 L .37567 .05618 L .37578 .05618 L .37588 .05618 L .37607 .05618 L .37627 .05618 L .37647 .05618 L .37658 .05618 L .37668 .05618 L .37687 .05618 L .37707 .05618 L .37725 .05618 L .37742 .05618 L .3776 .05618 L .3778 .05618 L .378 .05618 L .37811 .05618 L .37821 .05618 L .37843 .05618 L .37854 .05618 L .37865 .05618 L .37884 .05618 L .37905 .05618 L .37925 .05618 L .37943 .05618 L .3796 .05618 L .37979 .05618 L .37996 .05618 L .38012 .05618 L .3803 .05618 L .3805 .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 .05618 L .3912 .05618 L .39142 .05618 L .39153 .05618 L .39164 .05618 L .39185 .05618 L .39205 .05618 L .39222 .05618 L .39241 .05618 L .3926 .05618 L .39278 .05618 L .39296 .05618 L .39311 .05618 L .39328 .05618 L .39346 .05618 L .39365 .05618 L .39384 .05618 L .39403 .05618 L .3942 .05618 L .3944 .05618 L .39451 .05618 L .39461 .05618 L .3948 .05618 L .395 .05618 L .39519 .05618 L .39541 .05618 L .39561 .05618 L .39579 .05618 L .39598 .05618 L .39615 .05618 L .39634 .05618 L .39652 .05618 L .39672 .05618 L .39693 .05618 L .39711 .05618 L .3973 .05618 L .39752 .05618 L .39764 .05618 L .39774 .05618 L Mistroke .39795 .05618 L .39815 .05618 L .39832 .05618 L .39851 .05618 L .3987 .05618 L .39889 .05618 L .39906 .05618 L .39921 .05618 L .39939 .05618 L .39957 .05618 L .39975 .05618 L .39995 .05618 L .40013 .05618 L .4003 .05618 L .4005 .05618 L .40061 .05618 L .40071 .05618 L .4009 .05618 L .4011 .05618 L .4013 .05618 L .40141 .05618 L .40151 .05618 L .4017 .05618 L .4019 .05618 L .40208 .05618 L .40225 .05618 L .40243 .05618 L .40263 .05618 L .40283 .05618 L .40294 .05618 L .40304 .05618 L .40325 .05618 L .40337 .05618 L .40348 .05618 L .40367 .05618 L .40388 .05618 L .40408 .05618 L .40426 .05618 L .40443 .05618 L .40462 .05618 L .40479 .05618 L .40495 .05618 L .40513 .05618 L .40533 .05618 L .40552 .05618 L .4057 .05618 L .4059 .05618 L .40608 .05618 L .40625 .05618 L .40643 .05618 L Mistroke .40663 .05618 L .40684 .05618 L .40702 .05618 L .40721 .05618 L .40743 .05618 L .40762 .05618 L .40772 .05618 L .40783 .05618 L .40795 .05618 L .40806 .05618 L .40826 .05618 L .40845 .05618 L .40865 .05618 L .40886 .05618 L .40904 .05618 L .40923 .05618 L .40941 .05618 L .40958 .05618 L .40977 .05618 L .40998 .05618 L .41018 .05618 L .41036 .05618 L .41055 .05618 L .41076 .05618 L .41096 .05618 L .41114 .05618 L .41135 .05618 L .41147 .05618 L .41158 .05618 L .41178 .05618 L .4119 .05618 L .412 .05618 L .41211 .05618 L .41222 .05618 L .41243 .05618 L .41254 .05618 L .41265 .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 .16855 L .42097 .16855 L .42134 .16855 L .42298 .16855 L .42593 .16855 L .43239 .16855 L .4386 .16855 L .44521 .16855 L .45158 .16855 L .45771 .16855 L .46423 .16855 L .4705 .16855 L .47717 .16855 L .48359 .16855 L .48978 .16855 L .49635 .16855 L .50268 .16855 L Mistroke .50877 .16855 L .51526 .16855 L .52149 .16855 L .52813 .16855 L .53452 .16855 L .54066 .16855 L .5472 .16855 L .5535 .16855 L .56019 .16855 L .56664 .16855 L .57284 .16855 L .57605 .16855 L .57767 .16855 L .57811 .16855 L .57858 .16855 L .57881 .16855 L .57903 .16855 L .57923 .16855 L .57934 .16855 L .57944 .05618 L .57963 .05618 L .57983 .05618 L .58 .05618 L .58019 .05618 L .58039 .05618 L .5805 .05618 L .5806 .05618 L .5808 .05618 L .58099 .05618 L .58116 .05618 L .58135 .05618 L .58151 .05618 L .58169 .05618 L .58187 .05618 L .58208 .05618 L .58227 .05618 L .58244 .05618 L .58265 .05618 L .58276 .05618 L .58286 .05618 L .58307 .05618 L .58326 .05618 L .58336 .05618 L .58348 .05618 L .58368 .05618 L .5838 .05618 L .5839 .05618 L .58402 .05618 L .58414 .05618 L .58435 .05618 L Mistroke .58447 .05618 L .58458 .05618 L .58478 .05618 L .58499 .05618 L .58518 .05618 L .58536 .05618 L .58555 .05618 L .58576 .05618 L .58596 .05618 L .58615 .05618 L .58636 .05618 L .58656 .05618 L .58674 .05618 L .58692 .05618 L .5871 .05618 L .5873 .05618 L .5875 .05618 L .58761 .05618 L .58772 .05618 L .58792 .05618 L .58811 .05618 L .58821 .05618 L .58833 .05618 L .58853 .05618 L .58865 .05618 L .58877 .05618 L .58888 .05618 L .58899 .05618 L .5892 .05618 L .5894 .05618 L .58951 .05618 L .58962 .05618 L .58974 .05618 L .58985 .05618 L .58996 .05618 L .59008 .05618 L .59029 .05618 L .5904 .05618 L .59051 .05618 L .59063 .05618 L .59076 .05618 L .59097 .05618 L .59109 .05618 L .5912 .05618 L .5914 .05618 L .59151 .05618 L .59161 .05618 L .5918 .05618 L .59201 .05618 L .59221 .05618 L Mistroke .59239 .05618 L .59259 .05618 L .59278 .05618 L .59296 .05618 L .59314 .05618 L .59335 .05618 L .59345 .05618 L .59357 .05618 L .59377 .05618 L .59396 .05618 L .59413 .05618 L .59432 .05618 L .59448 .05618 L .59466 .05618 L .59485 .05618 L .59505 .05618 L .59524 .05618 L .59542 .05618 L .59563 .05618 L .59573 .05618 L .59585 .05618 L .59605 .05618 L .59624 .05618 L .59635 .05618 L .59646 .05618 L .59667 .05618 L .59678 .05618 L .59689 .05618 L .59701 .05618 L .59713 .05618 L .59734 .05618 L .59746 .05618 L .59757 .05618 L .59777 .05618 L .59798 .05618 L .59817 .05618 L .59834 .05618 L .59854 .05618 L .59875 .05618 L .59894 .05618 L .59905 .05618 L .59916 .05618 L .59937 .05618 L .59949 .05618 L .5996 .05618 L .59978 .05618 L .59998 .05618 L .60019 .05618 L .60039 .05618 L .6005 .05618 L Mistroke .60062 .05618 L .60073 .05618 L .60084 .05618 L .60104 .05618 L .60125 .05618 L .60136 .05618 L .60148 .05618 L .60169 .05618 L .60182 .05618 L .60194 .05618 L .60205 .05618 L .60217 .05618 L .60237 .05618 L .60256 .05618 L .60276 .05618 L .60288 .05618 L .60299 .05618 L .60319 .05618 L .6033 .05618 L .60341 .05618 L .60352 .05618 L .60362 .05618 L .60374 .05618 L .60385 .05618 L .60404 .05618 L .60424 .05618 L .60441 .05618 L .6046 .05618 L .6048 .05618 L .60492 .05618 L .60502 .05618 L .60522 .05618 L .60541 .05618 L .60561 .05618 L .60573 .05618 L .60583 .05618 L .60602 .05618 L .60622 .05618 L .6064 .05618 L .60657 .05618 L .60676 .05618 L .60696 .05618 L .60717 .05618 L .60729 .05618 L .6074 .05618 L .6076 .05618 L .60771 .05618 L .60782 .05618 L .60801 .05618 L .60822 .05618 L Mistroke .60842 .05618 L .6086 .05618 L .60878 .05618 L .60896 .05618 L .60913 .05618 L .60929 .05618 L .60948 .05618 L .60968 .05618 L .60987 .05618 L .61005 .05618 L .61023 .05618 L .6104 .05618 L .61058 .05618 L .61078 .05618 L .61099 .05618 L .61119 .05618 L .61137 .05618 L .61157 .05618 L .61167 .05618 L .61178 .05618 L .61198 .05618 L .61219 .05618 L .61231 .05618 L .61242 .05618 L .61263 .05618 L .61281 .05618 L .61292 .05618 L .61303 .05618 L .61323 .05618 L .61341 .05618 L .61361 .05618 L .61382 .05618 L .61402 .05618 L .6142 .05618 L .61436 .05618 L .61455 .05618 L .61474 .05618 L .61495 .05618 L .61515 .05618 L .61525 .05618 L .61537 .05618 L .61558 .05618 L .61577 .05618 L .61598 .05618 L .61616 .05618 L .61636 .05618 L .61647 .05618 L .61659 .05618 L .6168 .05618 L .61691 .05618 L Mistroke .61702 .05618 L .61714 .05618 L .61727 .05618 L .61748 .05618 L .61767 .05618 L .61779 .05618 L .61789 .05618 L .618 .05618 L .61812 .05618 L .61832 .05618 L .61843 .05618 L .61853 .05618 L .61872 .05618 L .61892 .05618 L .6191 .05618 L .61927 .05618 L .61946 .05618 L .61966 .05618 L .61987 .05618 L .61999 .05618 L .6201 .05618 L .6203 .05618 L .62041 .05618 L .62051 .05618 L .62071 .05618 L .62092 .05618 L .62111 .05618 L .6213 .05618 L .62147 .05618 L .62165 .05618 L .62182 .05618 L .62198 .05618 L .62217 .05618 L .62237 .05618 L .62256 .05618 L .62274 .05618 L .62292 .05618 L .62309 .05618 L .62327 .05618 L .62347 .05618 L .62367 .05618 L .62388 .05618 L .62406 .05618 L .62425 .05618 L .62447 .05618 L .62466 .05618 L .62477 .05618 L .62488 .05618 L .625 .05618 L .62511 .05618 L Mistroke .62531 .05618 L .62549 .05618 L .6256 .05618 L .62571 .05618 L .62591 .05618 L .62611 .05618 L .62629 .05618 L .6265 .05618 L .62669 .05618 L .62687 .05618 L .62704 .05618 L .62722 .05618 L .62742 .05618 L .62763 .05618 L .62782 .05618 L .62792 .05618 L .62804 .05618 L .62825 .05618 L .62845 .05618 L .62865 .05618 L .62883 .05618 L .62903 .05618 L .62914 .05618 L .62926 .05618 L .62946 .05618 L .62958 .05618 L .62969 .05618 L .62981 .05618 L .62994 .05618 L .63005 .05618 L .63017 .05618 L .63028 .05618 L .63038 .05618 L .63058 .05618 L .63079 .05618 L .63099 .05618 L .6311 .05618 L .6312 .05618 L .63139 .05618 L .63159 .05618 L .63177 .05618 L .63193 .05618 L .63212 .05618 L .63232 .05618 L .63252 .05618 L .63263 .05618 L .63273 .05618 L .63294 .05618 L .63306 .05618 L .63317 .05618 L Mistroke .63336 .05618 L .63357 .05618 L .63377 .05618 L .63395 .05618 L .63412 .05618 L .63431 .05618 L .63448 .05618 L .63464 .05618 L .63482 .05618 L .63502 .05618 L .63521 .05618 L .63539 .05618 L .63559 .05618 L .63577 .05618 L .63594 .05618 L .63612 .05618 L .63632 .05618 L .63653 .05618 L .63671 .05618 L .63691 .05618 L .63712 .05618 L .63731 .05618 L .63741 .05618 L .63752 .05618 L .63764 .05618 L .63775 .05618 L .63795 .05618 L .63814 .05618 L .63834 .05618 L .63855 .05618 L .63873 .05618 L .63892 .05618 L .6391 .05618 L .63927 .05618 L .63946 .05618 L .63967 .05618 L .63987 .05618 L .64005 .05618 L .64025 .05618 L .64046 .05618 L .64065 .05618 L .64083 .05618 L .64104 .05618 L .64116 .05618 L .64127 .05618 L .64148 .05618 L .64158 .05618 L .64169 .05618 L .6418 .05618 L .64191 .05618 L Mistroke .64212 .05618 L .64223 .05618 L .64234 .05618 L .64246 .05618 L .64258 .05618 L .64269 .05618 L .64281 .05618 L .64292 .05618 L .64302 .05618 L .64322 .05618 L .64342 .05618 L .64362 .05618 L .64383 .05618 L .64403 .05618 L .64422 .05618 L .6444 .05618 L .64457 .05618 L .64476 .05618 L .64494 .05618 L .64514 .05618 L .64535 .05618 L .64553 .05618 L .64572 .05618 L .64593 .05618 L .64605 .05618 L .64616 .05618 L .64637 .05618 L .64657 .05618 L .64674 .05618 L .64693 .05618 L .64712 .05618 L .6473 .05618 L .64747 .05618 L .64763 .05618 L .6478 .05618 L .64798 .05618 L .64817 .05618 L .64836 .05618 L .64855 .05618 L .64872 .05618 L .64891 .05618 L .64903 .05618 L .64913 .05618 L .64932 .05618 L .64952 .05618 L .64971 .05618 L .64993 .05618 L .65013 .05618 L .65031 .05618 L .6505 .05618 L Mistroke .65067 .05618 L .65086 .05618 L .65104 .05618 L .65124 .05618 L .65145 .05618 L .65163 .05618 L .65182 .05618 L .65204 .05618 L .65216 .05618 L .65226 .05618 L .65247 .05618 L .65267 .05618 L .65284 .05618 L .65303 .05618 L .65322 .05618 L .65341 .05618 L .65358 .05618 L .65373 .05618 L .65392 .05618 L .65409 .05618 L .65427 .05618 L .65447 .05618 L .65465 .05618 L .65482 .05618 L .65502 .05618 L .65513 .05618 L .65523 .05618 L .65542 .05618 L .65562 .05618 L .65582 .05618 L .65593 .05618 L .65603 .05618 L .65622 .05618 L .65642 .05618 L .6566 .05618 L .65677 .05618 L .65695 .05618 L .65715 .05618 L .65735 .05618 L .65746 .05618 L .65756 .05618 L .65777 .05618 L .65789 .05618 L .658 .05618 L .65819 .05618 L .6584 .05618 L .6586 .05618 L .65878 .05618 L .65895 .05618 L .65914 .05618 L Mistroke .65931 .05618 L .65947 .05618 L .65965 .05618 L .65985 .05618 L .66004 .05618 L .66022 .05618 L .66042 .05618 L .6606 .05618 L .66077 .05618 L .66095 .05618 L .66115 .05618 L .66136 .05618 L .66154 .05618 L .66174 .05618 L .66195 .05618 L .66214 .05618 L .66224 .05618 L .66235 .05618 L .66247 .05618 L .66258 .05618 L .66278 .05618 L .66297 .05618 L .66317 .05618 L .66338 .05618 L .66356 .05618 L .66375 .05618 L .66393 .05618 L .6641 .05618 L .66429 .05618 L .6645 .05618 L .6647 .05618 L .66488 .05618 L .66508 .05618 L .66528 .05618 L .66548 .05618 L .66566 .05618 L .66587 .05618 L .66599 .05618 L .6661 .05618 L .6663 .05618 L .66642 .05618 L .66652 .05618 L .66663 .05618 L .66674 .05618 L .66695 .05618 L .66706 .05618 L .66717 .05618 L .66729 .05618 L .66741 .05618 L .66752 .05618 L Mistroke .66764 .05618 L .66775 .05618 L .66785 .05618 L .66805 .05618 L .66825 .05618 L .66845 .05618 L .66866 .05618 L .66886 .05618 L .66904 .05618 L .66923 .05618 L .66939 .05618 L .66959 .05618 L .66977 .05618 L .66997 .05618 L .67017 .05618 L .67035 .05618 L .67055 .05618 L .67076 .05618 L .67088 .05618 L .67099 .05618 L .6712 .05618 L .6714 .05618 L .67157 .05618 L .67175 .05618 L .67195 .05618 L .67213 .05618 L .6723 .05618 L .67246 .05618 L .67263 .05618 L .67281 .05618 L .67299 .05618 L .67319 .05618 L .67337 .05618 L .67354 .05618 L .67374 .05618 L .67385 .05618 L .67396 .05618 L .67414 .05618 L .67434 .05618 L .67454 .05618 L .67475 .05618 L .67495 .05618 L .67514 .05618 L .67532 .05618 L .67549 .05618 L .67568 .05618 L .67586 .05618 L .67606 .05618 L .67627 .05618 L .67645 .05618 L Mistroke .67665 .05618 L .67686 .05618 L .67698 .05618 L .67709 .05618 L .6773 .05618 L .6775 .05618 L .67767 .05618 L .67785 .05618 L .67805 .05618 L .67823 .05618 L .6784 .05618 L .67856 .05618 L .67873 .05618 L .67891 .05618 L .6791 .05618 L .67929 .05618 L .67948 .05618 L .67965 .05618 L .67984 .05618 L .67995 .05618 L .68006 .05618 L .68025 .05618 L .68045 .05618 L .68064 .05618 L .68075 .05618 L .68086 .05618 L .68104 .05618 L .68124 .05618 L .68142 .05618 L .68159 .05618 L .68177 .05618 L .68197 .05618 L .68217 .05618 L .68228 .05618 L .68239 .05618 L .6826 .05618 L .68272 .05618 L .68282 .05618 L .68302 .05618 L .68323 .05618 L .68342 .05618 L .68361 .05618 L .68378 .05618 L .68396 .05618 L .68413 .05618 L .68429 .05618 L .68447 .05618 L .68467 .05618 L .68486 .05618 L .68504 .05618 L Mistroke .68524 .05618 L .68542 .05618 L .68559 .05618 L .68577 .05618 L .68597 .05618 L .68618 .05618 L .68636 .05618 L .68656 .05618 L .68677 .05618 L .68696 .05618 L .68706 .05618 L .68718 .05618 L .68729 .05618 L .6874 .05618 L .6876 .05618 L .68779 .05618 L .68799 .05618 L .6882 .05618 L .68838 .05618 L .68857 .05618 L .68875 .05618 L .68892 .05618 L .68911 .05618 L .68932 .05618 L .68952 .05618 L .6897 .05618 L .6899 .05618 L .6901 .05618 L .6903 .05618 L .69048 .05618 L .69069 .05618 L .69081 .05618 L .69092 .05618 L .69112 .05618 L .69124 .05618 L .69134 .05618 L .69145 .05618 L .69156 .05618 L .69177 .05618 L .69188 .05618 L .69199 .05618 L .69211 .05618 L .69223 .05618 L .69234 .05618 L .69246 .05618 L .69257 .05618 L .69267 .05618 L .69287 .05618 L .69307 .05618 L .69327 .05618 L Mistroke .69348 .05618 L .69368 .05618 L .69386 .05618 L .69405 .05618 L .69421 .05618 L .6944 .05618 L .69459 .05618 L .69478 .05618 L .69499 .05618 L .69517 .05618 L .69537 .05618 L .69558 .05618 L .6957 .05618 L .69581 .05618 L .69602 .05618 L .69622 .05618 L .69638 .05618 L .69657 .05618 L .69677 .05618 L .69695 .05618 L .69712 .05618 L .69728 .05618 L .69745 .05618 L .69763 .05618 L .69781 .05618 L .69801 .05618 L .69819 .05618 L .69836 .05618 L .69856 .05618 L .69867 .05618 L .69877 .05618 L .69896 .05618 L .69916 .05618 L .69936 .05618 L .69957 .05618 L .69977 .05618 L .69996 .05618 L .70014 .05618 L .70031 .05618 L .7005 .05618 L .70068 .05618 L .70088 .05618 L .70109 .05618 L .70127 .05618 L .70147 .05618 L .70168 .05618 L .7018 .05618 L .7019 .05618 L .70212 .05618 L .70231 .05618 L Mistroke .70248 .05618 L .70267 .05618 L .70287 .05618 L .70305 .05618 L .70322 .05618 L .70338 .05618 L .70355 .05618 L .70373 .05618 L .70391 .05618 L .70411 .05618 L .70429 .05618 L .70446 .05618 L .70466 .05618 L .70477 .05618 L .70487 .05618 L .70506 .05618 L .70526 .05618 L .70546 .05618 L .70567 .05618 L .70587 .05618 L .70606 .05618 L .70623 .05618 L .70641 .05618 L .7066 .05618 L .70679 .05618 L .70699 .05618 L .7072 .05618 L .70738 .05618 L .70757 .05618 L .70778 .05618 L .7079 .05618 L .70801 .05618 L .70822 .05618 L .70842 .05618 L .70859 .05618 L .70878 .05618 L .70897 .05618 L .70916 .05618 L .70933 .05618 L .70948 .05618 L .70966 .05618 L .70984 .05618 L .71002 .05618 L .71022 .05618 L .7104 .05618 L .71057 .05618 L .71077 .05618 L .71088 .05618 L .71098 .05618 L .71117 .05618 L Mistroke .71137 .05618 L .71157 .05618 L .71168 .05618 L .71178 .05618 L .71197 .05618 L .71217 .05618 L .71235 .05618 L .71252 .05618 L .7127 .05618 L .7129 .05618 L .7131 .05618 L .71321 .05618 L .71331 .05618 L .71353 .05618 L .71364 .05618 L .71375 .05618 L .71395 .05618 L .71416 .05618 L .71435 .05618 L .71454 .05618 L .71471 .05618 L .71489 .05618 L .71506 .05618 L .71522 .05618 L .7154 .05618 L .7156 .05618 L .71579 .05618 L .71597 .05618 L .71617 .05618 L .71636 .05618 L .71652 .05618 L .71671 .05618 L .7169 .05618 L .71711 .05618 L .71729 .05618 L .71749 .05618 L .7177 .05618 L .71789 .05618 L .718 .05618 L .71811 .05618 L .71823 .05618 L .71834 .05618 L .71854 .05618 L .71872 .05618 L .71892 .05618 L .71914 .05618 L .71932 .05618 L .71951 .05618 L .71969 .05618 L .71985 .05618 L Mistroke .72005 .05618 L .72026 .05618 L .72046 .05618 L .72064 .05618 L .72083 .05618 L .72104 .05618 L .72124 .05618 L .72142 .05618 L .72163 .05618 L .72175 .05618 L .72186 .05618 L .72206 .05618 L .72216 .05618 L .72228 .05618 L .72239 .05618 L .7225 .05618 L .72271 .05618 L .72282 .05618 L .72293 .05618 L .72304 .05618 L .72317 .05618 L .72328 .05618 L .7234 .05618 L .72351 .05618 L .72361 .05618 L .7238 .05618 L .72401 .05618 L .7242 .05618 L .72442 .05618 L .72462 .05618 L .7248 .05618 L .72499 .05618 L .72515 .05618 L .72535 .05618 L .72553 .05618 L .72573 .05618 L .72594 .05618 L .72611 .05618 L .72631 .05618 L .72652 .05618 L .72664 .05618 L .72675 .05618 L .72696 .05618 L .72716 .05618 L .72733 .05618 L .72751 .05618 L .72771 .05618 L .72789 .05618 L .72806 .05618 L .72822 .05618 L Mistroke .72839 .05618 L .72857 .05618 L .72876 .05618 L .72895 .05618 L .72914 .05618 L .7293 .05618 L .7295 .05618 L .72961 .05618 L .72972 .05618 L .72991 .05618 L .73011 .05618 L .7303 .05618 L .73052 .05618 L .73072 .05618 L .7309 .05618 L .73109 .05618 L .73125 .05618 L .73145 .05618 L .73163 .05618 L .73183 .05618 L .73204 .05618 L .73222 .05618 L .73241 .05618 L .73263 .05618 L .73275 .05618 L .73285 .05618 L .73306 .05618 L .73326 .05618 L .73343 .05618 L .73362 .05618 L .73382 .05618 L .734 .05618 L .73417 .05618 L .73433 .05618 L .73451 .05618 L .73468 .05618 L .73486 .05618 L .73506 .05618 L .73524 .05618 L .73541 .05618 L .73561 .05618 L .73572 .05618 L .73582 .05618 L .73601 .05618 L .73621 .05618 L .73641 .05618 L .73652 .05618 L .73662 .05618 L .73681 .05618 L .73701 .05618 L Mistroke .73719 .05618 L .73736 .05618 L .73754 .05618 L .73774 .05618 L .73794 .05618 L .73805 .05618 L .73816 .05618 L .73837 .05618 L .73849 .05618 L .73859 .05618 L .73879 .05618 L .739 .05618 L .73919 .05618 L .73938 .05618 L .73955 .05618 L .73973 .05618 L .7399 .05618 L .74006 .05618 L .74024 .05618 L .74044 .05618 L .74063 .05618 L .74081 .05618 L .74101 .05618 L .7412 .05618 L .74136 .05618 L .74155 .05618 L .74174 .05618 L .74195 .05618 L .74213 .05618 L .74233 .05618 L .74254 .05618 L .74273 .05618 L .74284 .05618 L .74295 .05618 L .74307 .05618 L .74317 .05618 L .74338 .05618 L .74356 .05618 L .74376 .05618 L .74398 .05618 L .74416 .05618 L .74435 .05618 L .74453 .05618 L .74469 .05618 L .74489 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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. (", StyleBox["Warning", FontWeight->"Bold"], ": some states may be separated by very small energies.)", "\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. Try modifying the height of the step barrier. What \ affect does this have on 1) the number of states with energies lower than the \ barrier, 2) the energies of these states, 3) the degree of barrier \ penetration?\n5. Try modifying the width of the step barrier. What affect \ does this have on 1) the number of states with energies lower than the \ barrier, 2) the energies of these states, 3) the degree of barrier \ penetration?\n\n5. Find at least two states for which the energy is ", StyleBox["greater", FontSlant->"Italic"], " than the step potential.\n6. How does the particle's ", StyleBox["wave length", FontSlant->"Italic"], " vary?\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?" }], "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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