Approximation to the solution of the Cauchy problem for a smoothed Schrödinger-Poisson equation in a magnetic field (Q2577300)

The paper presents the construction of approximations to the Cauchy problem for the equation describing the evolution of the wave function of a charged quantum-mechanical particle moving in a constant magnetic field under the action of an external potential and the field of a self-consistent potential, the latter being a smoothed version of the Coulomb potential. The main result is the uniform estimate for the difference between the exact and the approximate solution defined in terms of the Fourier-Gauss transform.