getEs()

void getEs(double E[],int nmax,double Elower,double V[],
           double r[],double dr[],int N)

Output:

• E[n]: linear array of energies of states with n=0 nodes through n=nmax nodes (inclusive!)

Input:

• nmax: maximum number of nodes sought
• Elower: energy guaranteed to be lower than any valid solutions
• V[]: effective potential on grid
• r[], dr[], N: standard grid information

Write a routine of the above prototype in ``physics.c'' to return the energies of the electronic states with zero through nmax nodes in the potential V[] to a precision of TOL, which you should set at the top of ``physics.c'' with a statement like

#define TOL (1.e-12)

The purpose of doing this is that you should never bury ``magic constants'' in your code, but rather define them in a single, centralized location where they are easily identified and changed.

Your routine should use rtbisp480() in conjunction with func_SchrodingerNodes() to first locate appropriate bounding energies, and then use zriddrp480 to find the solution to high precision.

A workable code fragment (but not the most efficient - you should try to do better) is

  /* Loop to get states */
  for (n=0; n<=nmax; n++) {
    /* Get E1 as an energy with n nodes */
    E1=rtbisp480(func_SchrodingerNodes,Elower,0.,TOL,n,V,r,dr,N);

    /* Get E2 as an energy with n+1 nodes */
    E2=rtbisp480(func_SchrodingerNodes,Elower,0.,TOL,n+1,V,r,dr,N);

    /* Now, get the solution, which is in between! */
    E[n]=zriddrp480(func_Schrodinger,E1,E2,TOL,0,V,r,dr,N);  
  }

Note: All solutions will have E<0, so using [Elower,0.] as the bounds for the rtbisp480() searches is guaranteed to work!