(************** 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). 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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[ 107864, 3779]*) (*NotebookOutlinePosition[ 108528, 3802]*) (* CellTagsIndexPosition[ 108484, 3798]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(\[Rho][r_]\ = \ \(-\((4 q/a^3)\)\)\ r^2\ Exp[\(-2\)\ r/a]\)], "Input"], Cell[BoxData[ \(\(-\(\(4\ \[ExponentialE]\^\(-\(\(2\ r\)\/a\)\)\ q\ \ r\^2\)\/a\^3\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(v[r_]\ = \ Integrate[\[Rho][x], {x, 0, r}, Assumptions \[Rule] a > 0]/r + Integrate[\[Rho][x]/x, {x, r, Infinity}, Assumptions \[Rule] a > 0]\)], "Input"], Cell[BoxData[ 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.01472 L .0802 .01472 L .08095 .01472 L .08166 .01472 L .08291 .01472 L .08362 .01472 L .08427 .01472 L .08544 .01472 L .08669 .01472 L .08787 .01472 L .08896 .01472 L .09016 .01472 L .09148 .01472 L .09214 .01472 L .09285 .01472 L .09413 .01472 L .09483 .01472 L .09548 .01472 L .09619 .01472 L .09695 .01472 L .09821 .01472 L .09893 .01472 L .09961 .01472 L .10086 .01472 L .10201 .01472 L .10333 .01472 L .10458 .01472 L .10572 .01472 L .10694 .01472 L .1081 .01472 L .10916 .01472 L .11033 .01472 L .11162 .01472 L .11227 .01472 L .11297 .01472 L .11422 .01472 L .11491 .01472 L .11554 .01472 L .11624 .01472 L .11698 .01472 L .11822 .01472 L .11892 .01472 L Mistroke .11958 .01472 L .12081 .01472 L .12194 .01472 L .12323 .01472 L .12446 .01472 L .12562 .01472 L .12668 .01472 L .12789 .01472 L .12903 .01472 L .13009 .01472 L .13107 .01472 L .13214 .01472 L .13327 .01472 L .13441 .01472 L .13564 .01472 L .1368 .01472 L .13785 .01472 L .13909 .01472 L .13979 .01472 L .14043 .01472 L .14162 .01472 L .14288 .01472 L .14402 .01472 L .14526 .01472 L .14656 .01472 L .14777 .01472 L .14891 .01472 L .14994 .01472 L .15113 .01472 L .15226 .01472 L .15348 .01472 L .15478 .01472 L .15589 .01472 L .15711 .01472 L .15842 .01472 L .15915 .01472 L .15982 .01472 L .16113 .01472 L .16236 .01472 L .16352 .01472 L .16456 .01472 L .16577 .01472 L .1669 .01472 L .16796 .01472 L .16893 .01472 L .16999 .01472 L .17111 .01472 L .17225 .01472 L .17347 .01472 L .17462 .01472 L Mistroke .17566 .01472 L .17689 .01472 L .17758 .01472 L .17823 .01472 L .1794 .01472 L .18065 .01472 L .18185 .01472 L .18316 .01472 L .18441 .01472 L .18556 .01472 L .1867 .01472 L .18773 .01472 L .18893 .01472 L .19005 .01472 L .19128 .01472 L .19258 .01472 L .19369 .01472 L .19491 .01472 L .19623 .01472 L .19696 .01472 L .19763 .01472 L .19894 .01472 L .20017 .01472 L .20122 .01472 L .20238 .01472 L .20359 .01472 L .20472 .01472 L .20578 .01472 L .20675 .01472 L .20781 .01472 L .20894 .01472 L .21008 .01472 L .21129 .01472 L .21244 .01472 L .21349 .01472 L .21472 .01472 L .21541 .01472 L .21605 .01472 L .21723 .01472 L .21847 .01472 L .21968 .01472 L .221 .01472 L .22224 .01472 L .2234 .01472 L .22454 .01472 L .22558 .01472 L .22677 .01472 L .2279 .01472 L .22914 .01472 L .23044 .01472 L Mistroke .23155 .01472 L .23277 .01472 L .23409 .01472 L .23482 .01472 L .2355 .01472 L .2368 .01472 L .23804 .01472 L .23909 .01472 L .24025 .01472 L .24146 .01472 L .2426 .01472 L .24365 .01472 L .24462 .01472 L .24569 .01472 L .24681 .01472 L .24795 .01472 L .24917 .01472 L .25032 .01472 L .25137 .01472 L .2526 .01472 L .25329 .01472 L .25393 .01472 L .2551 .01472 L .25635 .01472 L .25756 .01472 L .25888 .01472 L .26013 .01472 L .26129 .01472 L .26233 .01472 L .26348 .01472 L .26467 .01472 L .2658 .01472 L .26704 .01472 L .26835 .01472 L .26946 .01472 L .27068 .01472 L .272 .01472 L .27274 .01472 L .27341 .01472 L .27472 .01472 L .27595 .01472 L .27701 .01472 L .27817 .01472 L .27938 .01472 L .28052 .01472 L .28158 .01472 L .28255 .01472 L .28367 .01472 L .28474 .01472 L .28588 .01472 L Mistroke .2871 .01472 L .28825 .01472 L .2893 .01472 L .29053 .01472 L .29122 .01472 L .29186 .01472 L .29303 .01472 L .29427 .01472 L .29549 .01472 L .29618 .01472 L .29682 .01472 L .29799 .01472 L .29923 .01472 L .30034 .01472 L .30138 .01472 L .30252 .01472 L .30375 .01472 L .30499 .01472 L .30569 .01472 L .30634 .01472 L .30765 .01472 L .30839 .01472 L .30906 .01472 L .31026 .01472 L .31156 .01472 L .31278 .01472 L .31392 .01472 L .31497 .01472 L .31611 .01472 L .31718 .01472 L .31816 .01472 L .3193 .01472 L .32055 .01472 L .32173 .01472 L .32282 .01472 L .32406 .01472 L .32522 .01472 L .32626 .01472 L .32739 .01472 L .32862 .01472 L .32992 .01472 L .33103 .01472 L .33225 .01472 L .33356 .01472 L .33477 .01472 L .33541 .01472 L .3361 .01472 L .33683 .01472 L .33751 .01472 L .33876 .01472 L Mistroke .33991 .01472 L .34123 .01472 L .34249 .60332 L .3436 .59921 L .3448 .59488 L .34694 .5872 L .35181 .57035 L .37274 .50569 L .41429 .40675 L .45434 .33721 L .49286 .28641 L .53384 .24451 L .5733 .21269 L .61125 .18794 L .63238 .17612 L .64238 .17094 L .65165 .16636 L .65628 .16415 L .65741 .16362 L .65862 .16305 L .65932 .01472 L .65996 .01472 L .66121 .01472 L .66246 .01472 L .66363 .01472 L .66491 .01472 L .66562 .01472 L .66627 .01472 L .66759 .01472 L .66833 .01472 L .66902 .01472 L .67028 .01472 L .67091 .01472 L .67161 .01472 L .67287 .01472 L .67407 .01472 L .67515 .01472 L .67632 .01472 L .67759 .01472 L .6783 .01472 L .67895 .01472 L .6802 .01472 L .68138 .01472 L .6825 .01472 L .68368 .01472 L .68468 .01472 L .68578 .01472 L .68697 .01472 L .68824 .01472 L .68944 .01472 L Mistroke .69053 .01472 L .69171 .01472 L .69282 .01472 L .69404 .01472 L .69535 .01472 L .69665 .01472 L .6973 .01472 L .69802 .01472 L .69928 .01472 L .70046 .01472 L .70166 .01472 L .70279 .01472 L .7038 .01472 L .7049 .01472 L .7061 .01472 L .70737 .01472 L .70845 .01472 L .70964 .01472 L .7103 .01472 L .71103 .01472 L .71234 .01472 L .71363 .01472 L .71481 .01472 L .71554 .01472 L .71623 .01472 L .71751 .01472 L .71823 .01472 L .71888 .01472 L .71961 .01472 L .72037 .01472 L .72157 .01472 L .72285 .01472 L .72406 .01472 L .72516 .01472 L .72645 .01472 L .72718 .01472 L .72786 .01472 L .72909 .01472 L .73041 .01472 L .73161 .01472 L .73293 .01472 L .73417 .01472 L .73532 .01472 L .73646 .01472 L .7375 .01472 L .73869 .01472 L .73982 .01472 L .74105 .01472 L .74235 .01472 L .74346 .01472 L Mistroke .74468 .01472 L .74599 .01472 L .74673 .01472 L .7474 .01472 L .7487 .01472 L .74994 .01472 L .75099 .01472 L .75214 .01472 L .75335 .01472 L .75449 .01472 L .75555 .01472 L .75652 .01472 L .75758 .01472 L .7587 .01472 L .75984 .01472 L .76106 .01472 L .76221 .01472 L .76326 .01472 L .76448 .01472 L .76518 .01472 L .76582 .01472 L .76699 .01472 L .76824 .01472 L .76945 .01472 L .77077 .01472 L .77201 .01472 L .77317 .01472 L .77431 .01472 L .77535 .01472 L .77654 .01472 L .77767 .01472 L .77891 .01472 L .78021 .01472 L .78132 .01472 L .78254 .01472 L .78386 .01472 L .7846 .01472 L .78527 .01472 L .78657 .01472 L .78781 .01472 L .78886 .01472 L .79002 .01472 L .79123 .01472 L .79237 .01472 L .79343 .01472 L .7944 .01472 L .79546 .01472 L .79658 .01472 L .79773 .01472 L .79895 .01472 L Mistroke .8001 .01472 L .80114 .01472 L .80237 .01472 L .80306 .01472 L .8037 .01472 L .80488 .01472 L .80612 .01472 L .80733 .01472 L .80802 .01472 L .80866 .01472 L .80982 .01472 L .81107 .01472 L .81217 .01472 L .81321 .01472 L .81435 .01472 L .81558 .01472 L .81681 .01472 L .81751 .01472 L .81816 .01472 L .81947 .01472 L .8202 .01472 L .82087 .01472 L .82207 .01472 L .82337 .01472 L .8246 .01472 L .82573 .01472 L .82678 .01472 L .82792 .01472 L .82899 .01472 L .82996 .01472 L .83111 .01472 L .83235 .01472 L .83353 .01472 L .83463 .01472 L .83586 .01472 L .83702 .01472 L .83806 .01472 L .83919 .01472 L .84042 .01472 L .84172 .01472 L .84284 .01472 L .84405 .01472 L .84536 .01472 L .84657 .01472 L .8472 .01472 L .84789 .01472 L .84862 .01472 L .8493 .01472 L .85055 .01472 L .85169 .01472 L Mistroke .85295 .01472 L .85427 .01472 L .85538 .01472 L .85657 .01472 L .85769 .01472 L .85871 .01472 L .85991 .01472 L .86121 .01472 L .86244 .01472 L .86358 .01472 L .86478 .01472 L .86608 .01472 L .8673 .01472 L .86842 .01472 L .86972 .01472 L .87046 .01472 L .87115 .01472 L .8724 .01472 L .8731 .01472 L .87374 .01472 L .87441 .01472 L .87513 .01472 L .8764 .01472 L .87711 .01472 L .87778 .01472 L .8785 .01472 L .87928 .01472 L .87995 .01472 L .88068 .01472 L .88137 .01472 L .88201 .01472 L .88322 .01472 L .88449 .01472 L .8857 .01472 L .88701 .01472 L .88825 .01472 L .8894 .01472 L .89054 .01472 L .89158 .01472 L .89277 .01472 L .8939 .01472 L .89513 .01472 L .89643 .01472 L .89754 .01472 L .89876 .01472 L .90007 .01472 L .9008 .01472 L .90148 .01472 L .90278 .01472 L .90402 .01472 L Mistroke .90506 .01472 L .90622 .01472 L .90743 .01472 L .90857 .01472 L .90962 .01472 L .91059 .01472 L .91166 .01472 L .91278 .01472 L .91392 .01472 L .91513 .01472 L .91628 .01472 L .91733 .01472 L .91856 .01472 L .91925 .01472 L .91989 .01472 L .92107 .01472 L .92231 .01472 L .92352 .01472 L .92484 .01472 L .92608 .01472 L .92724 .01472 L .92838 .01472 L .92942 .01472 L .93061 .01472 L .93174 .01472 L .93297 .01472 L .93428 .01472 L .93539 .01472 L .93661 .01472 L .93792 .01472 L .93866 .01472 L .93933 .01472 L .94064 .01472 L .94187 .01472 L .94292 .01472 L .94408 .01472 L .9453 .01472 L .94643 .01472 L .94749 .01472 L .94846 .01472 L .94953 .01472 L .95065 .01472 L .95179 .01472 L .95301 .01472 L .95416 .01472 L .9552 .01472 L .95643 .01472 L .95713 .01472 L .95777 .01472 L .95894 .01472 L Mistroke .96018 .01472 L .96125 .01472 L .96227 .01472 L .96318 .01472 L .96417 .01472 L .96525 .01472 L .9664 .01472 L .96737 .01472 L .96846 .01472 L .96946 .01472 L .97037 .01472 L .97138 .01472 L .97244 .01472 L .97337 .01472 L .97423 .01472 L .97518 .01472 L .97619 .01472 L Mfstroke 0 0 0 r .02381 .01472 m .02499 .01472 L .02605 .01472 L .02729 .01472 L .02846 .01472 L .02954 .01472 L .03053 .01472 L .03163 .01472 L .03279 .01472 L .03395 .01472 L .0352 .01472 L .03638 .01472 L .03746 .01472 L .03873 .01472 L .03944 .01472 L .04011 .01472 L .04132 .01472 L .04262 .01472 L .04327 .01472 L .04396 .01472 L .04519 .01472 L .04588 .01472 L .04652 .01472 L .04722 .01472 L .04797 .01472 L .04862 .01472 L .04933 .01472 L .05061 .01472 L .05186 .01472 L .05302 .01472 L .05414 .01472 L .05519 .01472 L .05634 .01472 L .05759 .01472 L .05882 .01472 L .06012 .01472 L .06123 .01472 L .06244 .01472 L .06315 .01472 L .06381 .01472 L .06453 .01472 L .06529 .01472 L .06657 .01472 L .06729 .01472 L .06797 .01472 L .06924 .01472 L .0704 .01472 L .07103 .01472 L .07173 .01472 L .073 .01472 L Mistroke .07376 .01472 L .07448 .01472 L .07513 .01472 L .07583 .01472 L .0766 .01472 L .0774 .01472 L .07809 .01472 L .07885 .01472 L .07956 .01472 L .0802 .01472 L .08095 .01472 L .08166 .01472 L .08291 .01472 L .08362 .01472 L .08427 .01472 L .08544 .01472 L .08669 .01472 L .08787 .01472 L .08896 .01472 L .09016 .01472 L .09148 .01472 L .09214 .01472 L .09285 .01472 L .09413 .01472 L .09483 .01472 L .09548 .01472 L .09619 .01472 L .09695 .01472 L .09821 .01472 L .09893 .01472 L .09961 .01472 L .10086 .01472 L .10201 .01472 L .10333 .01472 L .10458 .01472 L .10572 .01472 L .10694 .01472 L .1081 .01472 L .10916 .01472 L .11033 .01472 L .11162 .01472 L .11227 .01472 L .11297 .01472 L .11422 .01472 L .11491 .01472 L .11554 .01472 L .11624 .01472 L .11698 .01472 L .11822 .01472 L .11892 .01472 L Mistroke .11958 .01472 L .12081 .01472 L .12194 .01472 L .12323 .01472 L .12446 .01472 L .12562 .01472 L .12668 .01472 L .12789 .01472 L .12903 .01472 L .13009 .01472 L .13107 .01472 L .13214 .01472 L .13327 .01472 L .13441 .01472 L .13564 .01472 L .1368 .01472 L .13785 .01472 L .13909 .01472 L .13979 .01472 L .14043 .01472 L .14162 .01472 L .14288 .01472 L .14402 .01472 L .14526 .01472 L .14656 .01472 L .14777 .01472 L .14891 .01472 L .14994 .01472 L .15113 .01472 L .15226 .01472 L .15348 .01472 L .15478 .01472 L .15589 .01472 L .15711 .01472 L .15842 .01472 L .15915 .01472 L .15982 .01472 L .16113 .01472 L .16236 .01472 L .16352 .01472 L .16456 .01472 L .16577 .01472 L .1669 .01472 L .16796 .01472 L .16893 .01472 L .16999 .01472 L .17111 .01472 L .17225 .01472 L .17347 .01472 L .17462 .01472 L Mistroke .17566 .01472 L .17689 .01472 L .17758 .01472 L .17823 .01472 L .1794 .01472 L .18065 .01472 L .18185 .01472 L .18316 .01472 L .18441 .01472 L .18556 .01472 L .1867 .01472 L .18773 .01472 L .18893 .01472 L .19005 .01472 L .19128 .01472 L .19258 .01472 L .19369 .01472 L .19491 .01472 L .19623 .01472 L .19696 .01472 L .19763 .01472 L .19894 .01472 L .20017 .01472 L .20122 .01472 L .20238 .01472 L .20359 .01472 L .20472 .01472 L .20578 .01472 L .20675 .01472 L .20781 .01472 L .20894 .01472 L .21008 .01472 L .21129 .01472 L .21244 .01472 L .21349 .01472 L .21472 .01472 L .21541 .01472 L .21605 .01472 L .21723 .01472 L .21847 .01472 L .21968 .01472 L .221 .01472 L .22224 .01472 L .2234 .01472 L .22454 .01472 L .22558 .01472 L .22677 .01472 L .2279 .01472 L .22914 .01472 L .23044 .01472 L Mistroke .23155 .01472 L .23277 .01472 L .23409 .01472 L .23482 .01472 L .2355 .01472 L .2368 .01472 L .23804 .01472 L .23909 .01472 L .24025 .01472 L .24146 .01472 L .2426 .01472 L .24365 .01472 L .24462 .01472 L .24569 .01472 L .24681 .01472 L .24795 .01472 L .24917 .01472 L .25032 .01472 L .25137 .01472 L .2526 .01472 L .25329 .01472 L .25393 .01472 L .2551 .01472 L .25635 .01472 L .25756 .01472 L .25888 .01472 L .26013 .01472 L .26129 .01472 L .26233 .01472 L .26348 .01472 L .26467 .01472 L .2658 .01472 L .26704 .01472 L .26835 .01472 L .26946 .01472 L .27068 .01472 L .272 .01472 L .27274 .01472 L .27341 .01472 L .27472 .01472 L .27595 .01472 L .27701 .01472 L .27817 .01472 L .27938 .01472 L .28052 .01472 L .28158 .01472 L .28255 .01472 L .28367 .01472 L .28474 .01472 L .28588 .01472 L Mistroke .2871 .01472 L .28825 .01472 L .2893 .01472 L .29053 .01472 L .29122 .01472 L .29186 .01472 L .29303 .01472 L .29427 .01472 L .29549 .01472 L .29618 .01472 L .29682 .01472 L .29799 .01472 L .29923 .01472 L .30034 .01472 L .30138 .01472 L .30252 .01472 L .30375 .01472 L .30499 .01472 L .30569 .01472 L .30634 .01472 L .30765 .01472 L .30839 .01472 L .30906 .01472 L .31026 .01472 L .31156 .01472 L .31278 .01472 L .31392 .01472 L .31497 .01472 L .31611 .01472 L .31718 .01472 L .31816 .01472 L .3193 .01472 L .32055 .01472 L .32173 .01472 L .32282 .01472 L .32406 .01472 L .32522 .01472 L .32626 .01472 L .32739 .01472 L .32862 .01472 L .32992 .01472 L .33103 .01472 L .33225 .01472 L .33356 .01472 L .33477 .01472 L .33541 .01472 L .3361 .01472 L .33683 .01472 L .33751 .01472 L .33876 .01472 L Mistroke .33991 .01472 L .34123 .01472 L .34249 .44093 L .3436 .43944 L .3448 .43787 L .34694 .43506 L .35181 .42882 L .37274 .40398 L .41429 .36255 L .45434 .3302 L 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