Recursion methods for solving the Schrödinger equation

The purpose of this study is to approximate the local density of states(LDOS) for a metal block by solving the Schrödinger equation in an efficient way. To make the code more effective different methods were implemented, for example trying to parallelize the process and to run the code solely on a GPU (Graphic Processing Unit). The conclusion that was drawn was that running the code in parallel over the different orbitals on a multicore central processing unit (CPU) is faster and thusmore efficient than running it in sequential order. Running the calculations on a GPU was determined to be slower because of inefficient use of its bandwidth due to individual indexing in matrices and vectors. Further tests using block versions of the same algorithm on GPUs couldbe of interest because of better use of the available bandwidth. These tests were not done due to time constraints