Fourth-order algorithms for solving local Schrödinger equations in a strong magnetic field

We describe an efficient numerical method for solving eigenvalue problems associated with the one-body Schrödinger equation or the Kohn-Sham equations in an arbitrarily strong uniform external magnetic field. The eigenvalue problem is solved in real space by using a fourth order, forward factorization of the evolution operator e-εH, which is significantly more efficient than conventional second-order algorithms. In particular, the magnetic field is solved exactly by the decomposition process. The algorithm is applicable to any external potential, in addition to the magnetic field. We envision its primary application in the area of electronic structure calculations of quantum dots.