Developing of Scientific Software Applications in Python. [Part] 1, Transformation of Hubbard Hamiltonian into the Matrix and its Diagonalization

In order to perform larger scale physics research in the area of superconductivity, we have developed an application that can transform the Hubbard Hamiltonian into a matrix and diagonalize it to find the selected model’s energy spectrum. For that purpose we have used the Python language and its wide ecosystem. This paper proves that selected tools are capable of creating scientific applications in a general sense. After a short introduction into the physics problem and the designed algorithm we will present the computer science problems and their solutions in creating usual scientific programs, in particular: performance and parallelization issues, storage of input data and the results, bottlenecks detections, as well as optimization and testing. The most interesting examples of the developing cycle will be described to give a prepared solution for implementing the other scientific software.