%%This M-file will generate the phase portrait for the Inverse Harmonic %%Oscillator Potential V=-1/2*Kx^2. %%Total Energy E is constant: clf; hold on; axis([-3 3 -3 3]); for E=-4:.25:4 if E >= 0 x=[-5:0.01:-0.01,0.01:0.01:5]; dx=gradient(x); v=sqrt(2*E-x.^2-1./x.^2); dv=gradient(v); plot(x,v,'black'); plot(x,-v,'black'); for i=1:length(v) if imag(v(i))==0 h=quiver(x(i),v(i),dx(i),dv(i)); i=quiver(-x(i),v(i),dx(i),-dv(i)); set(i,'LineWidth',3); set(i,'Color','black'); set(h,'LineWidth',3); set(h,'MarkerSize',10000); set(h,'Color','black'); break end end end if E <0 xmin=sqrt(-2*E); x=(xmin+.00001:0.01:4*xmin); v=sqrt(2*E-x.^2-1./x.^2); plot(x,v); plot(-x,v); plot(x,-v); plot(-x,-v); end end title('Phase Portrait for Potential V(x)=1