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Wave Propagation in Linear Media | re-examined

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Example 8.4.2<br />

1<br />

0.5<br />

-0.5<br />

-1<br />

8 Application of the quadratu<strong>re</strong> rout<strong>in</strong>e<br />

In[2]:= <strong>in</strong>itialtria = Table[fx,Phi[x,t,w,k,Shape->Tria]g,<br />

fx,-230,10,1.25g];<br />

ListPlot[<strong>in</strong>itialtria/.fx_,y_g:>fx,Re[y]g,PlotJo<strong>in</strong>ed->True];<br />

-200 -150 -100 -50<br />

1.5<br />

1<br />

0.5<br />

-0.5<br />

-1<br />

-1.5<br />

For the Gaussian wave, we need the additional parameter describ<strong>in</strong>g the variance of the<br />

probability distribution. We set it to one third of the distance between the maximum and<br />

the edge of the barrier.<br />

Example 8.4.3<br />

In[3]:= n = 6;<br />

<strong>in</strong>itialgauss = Table[fx,Phi[x,t,w,k,n,Shape->Gauss,<br />

PPo<strong>in</strong>ts->Truncate]g,fx,-230,10,1.25g];<br />

ListPlot[<strong>in</strong>itialgauss/.fx_,y_g:>fx,Re[y]g,PlotJo<strong>in</strong>ed->True,<br />

PlotRange->All];<br />

206

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