Mathematical analysis of the dimensional scaling technique for the Schrödinger equation with power-law potentials

Abstract

The dimensional scaling (D-scaling) technique is an innovative asymptotic expansion approach to study the multiparticle systems in molecular quantum mechanics. It enables the calculation of ground and excited state energies of quantum systems without having to solve the Schrödinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schrödinger equation with power-law potentials. By casting the D-scaling technique in an appropriate variational setting and studying the corresponding minimization problem, the D-scaling technique is justified rigorously. A new asymptotic dimensional expansion scheme is introduced to compute asymptotic expansions for ground state energies.