What you want to do is not necessarily impossible, but it is unlikely, and harder than you think.
First of all, you seem to underestimate what it takes to become a researcher. There is no uniform rule, as there are wildly different levels of talent, and also different areas require different levels of expertise to be able to produce research. That said, a ...
Based on the discussion in the comments, it seems that what is really needed is code that will produce the eigenvalues of the matrix $D_N$. We can produce this outcome with the following script:
N = 2^3;
D = circshift(eye(N),-1) + circshift(eye(N),1) - 2*eye(N);