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

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 Schrdinger equation. In this paper, we present a mathematical analysis of the D-scaling technique for the Schrdinger 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. 2010 American Institute of Physics.

Mathematical analysis of the dimensional scaling technique for the Schrodinger equation with power-law potentials Academic Article