Solving many-body Schrödinger equations with kinetic energy partition method

We present a general formulation of our previously developed kinetic energy partition (KEP) method for solving many-bodySchrödinger equations. In atomic physics, as well as in general molecular and solid state physics, solving many-electronSchrödinger equations is a very challenging task, often called Dirac's challenge. The central problem is how to properly handle the electron-electron Coulomb repulsion interactions. Using the KEP solution scheme, in addition to dividing the kinetic energy into partial terms, the electron-electron Coulomb interaction is also separated into parts to be associated with a “negative mass” kinetic energy term. Therefore, the full Hamiltonian can be expressed as a simple sum of subsystem Hamiltonians, each representing an effective one-body problem. Using a Hartree-like product in constructing the wave-function, we achieve fast convergence in the calculations of the ground state energies. First, the model Moshinsky atoms are used to illustrate the solution procedure. We then apply this new KEP method to harmonium atoms and obtain precise energies with an error less than 5% using only two basis functions from each subsystem. It is thus very promising that this methodology, when further extended, can be useful for general many-body systems.