Again, run the program with E=-0.5. Your results for the outward integration should agree with the analytic solution to about 4-5 decimal places (except for k>80). Because the Schrödinger equation determines the wave function only up to a constant normalization factor, the results for the inward integration will not match the analytic solution, but the ratio should be constant to within about 4-5 decimal places, except for numerical errors near the ends of the integration interval.
Note: The facts that V(r)=-1/r and r[0]=0 cause
numerical difficulties at the origin. To avoid this, ``schdebug.c'' uses
the change of variables map 
. Under this map, near
the origin 
, 
,
and 
. Thus, it is
mathematically correct to regard the offending term 
as zero at the origin. The
program ``schdebug.c'' achieves the same effect, but without the
division by zero and the NaN's, by simply setting V[0]=0 when
initializing the array V[].