Kinetic-energy density functional for a special shape-invariant potential of a one-dimensional two-level system

摘要

By introducing the concept of supersymmetry to quantum mechanics, several authors have shown that exactly soluble potentials, including all those well known, are easily constructed. Is the kinetic-energy density functional corresponding to these potentials a simple form? We show that the answer is no, even to the simplest one, the harmonic potential, if one builds the kinetic-energy density functional from the reduced density matrix.