Function space requirements for the single-electron functions within the multiparticle Schrödinger equation

Our previously described method to approximate the many-electron wavefunction in the multiparticle Schrodinger equation reduces this problem to operations on many single-electron functions. In this work, we analyze these operations to determine which function spaces are appropriate for various intermediate functions in order to bound the output. This knowledge then allows us to choose the function spaces in which to control the error of a numerical method for single-electron functions. We find that an efficient choice is to maintain the single-electron functions in L2 ∩ L4, the product of these functions in L1 ∩ L2, the Poisson kernel applied to the product in L4, a function times the Poisson kernel applied to the product in L2, and the nuclear potential times a function in L4/3. Due to the integral operator formulation, we do not require differentiability.