Simple Molecules and Variant Scalings

Tan and J. G. Loeser Department of Chemistry Oregon State University CorvalliS) OR 97331-4003. 

In atomic units, the non-relativistic Schiodinger equation of a system of N particles in D-dimensional Euclidean space is 

Our aim is to recast the equation in a form appropriate for analysis in the D— oo limit. Since this limit is a classical one, characterized by interparticle distances which are fixed relative to one another, we will use the interparticle distances. 

If we transform to the center of mass and restrict attention to spherically symmetric states, then the Laplacians can be rewritten in terms of the internal coordinates r.- 

As noted elsewhere [1,2], we can derive and interpret solutions more easily if we make a transformation which removes first derivative terms. This may be done by incorporating a factor related to the volume element, which we shall denote by J, into the wave function  

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