COPYRIGHT 2008, PRINCETON UNIVERSITY PRESS

differential equation applications 217✞/ / QuantumNumerov . java : solves Schroed eq via Numerov + Bisection Algor☎import java . io .∗ ;import ptolemy . plot .∗ ;public class QuantumNumerov {public static void main ( String [] argv ) {Plot myPlot = new Plot () ;myPlot. setTitle ("Schrodinger Eqn Numerov- Eigenfunction");myPlot. setXLabel ("x" );myPlot. setYLabel ("Y(x)") ;myPlot . setXRange(−1000,1000) ;myPlot. setColor ( false );PlotApplication app = new PlotApplication (myPlot) ;Plot myPlot1 = new Plot () ;myPlot1 . setTitle ("Schrodinger Eqn Numerov- Probability Density") ;myPlot1 . setXLabel ("x" );myPlot1 . setYLabel ("Y(x)^2") ;myPlot1 . setXRange(−1000,1000) ;myPlot1 . setYRange( −0.004,0.004) ;myPlot1 . setColor ( false );PlotApplication app1 = new PlotApplication (myPlot1 ) ;int i , istep , im, n, m, imax , nl , nr ;double dl=1e−8, h, min, max, e, e1 , de, xl0 , xr0 , xl , xr , f0 , f1 , sum, v, fact ;double ul [] = new double [1501] , ur[] = new double [1501] , k2l[]=new double [1501];double s[] = new double [1501] , k2r[] = new double [1501];n = 1501; m = 5; im = 0; imax = 100; xl0 = −1000; xr0 = 1000;h = ( xr0−xl0 )/(n−1) ;min = −0.001; max = −0.00085; e = min; de = 0.01;ul[0] = 0.0; ul[1] = 0.00001; ur[0] = 0.0; ur[1] = 0.00001;for (i = 0; i < n; ++i) { // Set up the potential k2xl = xl0+i∗h;xr = xr0−i ∗h;k2l [ i ] = (e−v(xl)) ;k2r [ i ] = (e−v(xr)) ;}im = 500; / / The matching pointnl = im+2;nr = n−im+1;numerov ( nl , h , k2l , ul ) ; numerov ( nr , h , k2r , ur ) ;fact= ur[nr−2]/ul [ im ] ; // Rescale the solutionfor ( i = 0; i < nl ; ++i ) ul[ i ] = fact∗ul [ i ];f0 = (ur[nr−1]+ul [ nl−1]−ur [nr−3]−ul [nl −3])/(2∗h∗ur [nr−2]) ; // Log derivistep = 0; // Bisection algor for the rootwhile ( Math . abs ( de ) > dl && istep < imax ) {e1 = e ;e = ( min+max) /2;for (i = 0; i < n; ++i) {k2l [ i ] = k2l [ i ]+(e−e1 ) ;k2r [ i ] = k2r [ i ]+(e−e1 ) ;}im=500;nl = im+2;nr = n−im+1;numerov ( nl , h , k2l , ul ) ; numerov ( nr , h , k2r , ur ) ;fact=ur[nr−2]/ul [ im ] ; // Rescale solutionfor ( i = 0; i < nl ; ++i ) ul[ i ] = fact∗ul [ i ];f1 = (ur[nr−1]+ul [ nl−1]−ur [nr−3]−ul [nl −3])/(2∗h∗ur [nr−2]) ; / / Log derif ((f0∗ f 1 ) < 0 ) { max = e ; de = max−min ; }else { min = e ; de = max−min ; f0 = f1 ; }istep = istep+1;}sum = 0 ;for (i = 0; i < n; ++i) { if (i > im) ul[i] = ur[n−i −1]; sum = sum+ul [ i ]∗ ul [ i ]; }sum = Math . sqrt (h∗sum) ;System . out . println ("istep=" +istep ) ;System . out . println ("e= "+ e+" de= "+de ) ;for ( i = 0; i < n; i = i+m) {−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 217