As discussed in lecture, our basic strategy to find the energies of
the atom is to set
and
at one end of our solution
(r=0 or
), define a function f(E) as the value
of
at the other end, and then seek the roots of f(E).
As discussed in class, there are a variety of methods for root finding, solving one equation in one unknown of the form f(x)=0. Computationally, these methods depend upon calling a function subroutine which returns the value of the function f(x) for any input value x. In this problem, we will implement versions of two of the Numerical Recipes subroutines for doing this, rtbisp480() and zriddrp480(). As with rk4p480(), we will also have to write a helper routine, which in this case we call func_Schrodinger().