Dimensional scaling and the quantum mechanical many-body problem

Summary A growing repertoire of electronic structure methods employ the spatial dimensionD as an interpolation or scaling parameter. It is advantageous to transform the Schrödinger equation to remove all dependence onD from the Jacobian volume element and the Laplacian operator; this introduces a centrifugal term, quadratic inD, that augments the effective potential. Here we explicitly formulate this procedure forS 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 solvableD limit and perturbation expansions about this limit. The other version casts the Jacobian and Laplacian into the familiar forms forD=3, and is particularly suited to calculations employing conventional Rayleigh-Ritz variational methods.