% A symmetric potential of width 4 and depth ~ 40.
function v1 = v1dkhead(x)

in = (abs(x) < (2 - eps)); % eps is a safety margin to avoid sqrt(negatives).
v1(!in) = 0;

ears = 75 - ( (8*x(in)).^2 - (4*x(in)).^4 ).^3;
head = 100*x(in).^2 + 20;
shoulders = 20*sqrt(4 - x(in).^2);

v1(in) = - min( shoulders, min(head, ears) );

if max(imag(v1)) != 0
   v1
   x
   error('Imaginary result in v1dkhead!')
end