DIMENSIONAL SCALING AND THE QUANTUM-MECHANICAL MANY-BODY PROBLEM

A growing repertoire of electronic structure methods employ the spatial dimension D as an interpolation or scaling parameter. It is advantageous to transform the Schrodinger equation to remove all dependence on D from the Jacobian volume element and the Laplacian operator; this introduces a centrifugal term, quadratic in D, that augments the effective potential. Here we explicitly formulate this procedure for S states of an arbitrary many-particle system, in two variants. One version reduces the Laplacian to a quasicartesian form, and is particularly suited to evaluating the exactly solvable D --> infinity limit and perturbation expansions about this limit. The other version casts the Jacobian and Laplacian into the familiar forms for D = 3, and is particularly suited to calculations employing conventional Rayleigh-Ritz variational methods.