## Potential-energy function of diatomic molecule

Hi there all, I have this problem which I have issues with; theres some stuff I need to do in C and any help would be much appreciated.

For V(o) = 36 i need to find the ground state energy and normalised ground state function using matrix methods. I am allowed to use Matlab to find the eigenvalues and vectors.
The matrix method includes numerical techniques where theres finite approximations.

This picture is a general solution; for this specific problem the potential V(i) = V(x(i)) and lambda is equal to E.
Through finite approximations using Taylors rule you get the matrix

Im guessing that the ground state energy is the eigenvalue for when phi(0) = 0 and the other eigenvalue will be when phi(L) = 0. Im guessing that the normalised ground state function would be the eigenvector of this matrix?
So through the theory of eigenvalue and eigenvectors, deltaxsquared*lambda will be an eigenvalue and the matrix phi(1) phi(2) etc is an eigenvector.
I effectively need to calculate the eigenvalues and eigenvectors of a symmetrix tridiagonal matrix... basically a Hermitian matrix and I am aware that the process for a Hermitian matrix is a lot simpler than for anti symmetric. NAG routines however are unfamiliar to me (they are meant to be used) I am allowed to use Matlab to calculate the eigenvalues and eigenvectors.
I also need to write a C program to find the ground state energy and normalised ground state function using the matching method. I am completely unfamiliar with the matching method in C and I am not being given a lot of help. Apparently you have to start with 2 independant solutions, rescale one curve so that they cross and vary E until both curves have the same slope at the crossing point. I am aware however that this is very ambiguous so any help would be very appreciated.
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