Wave-mechanics and the adhesion approximation
  The dynamical equations describing the evolution of a self-gravitating fluid of cold dark matter (CDM) can be written in the form of a Schrodinger equation coupled to a Poisson equation describing Newtonian gravity. It has recently been shown that, in the quasi-linear regime, the Schrodinger equation can be reduced to the exactly solvable free-particle Schrodinger equation. The free-particle Schrodinger equation forms the basis of a new approximation scheme -the free-particle approximation - that is capable of evolving cosmological density perturbations into the quasi-linear regime. The free-particle approximation is essentially an alternative to the adhesion model in which the artificial viscosity term in Burgers' equation is replaced by a non-linear term known as the quantum pressure. Simple one-dimensional tests of the free-particle method have yielded encouraging results. In this paper we comprehensively test the free-particle approximation in a more cosmologically relevant scenario by appealing to an N-body simulation. We compare our results with those obtained from two established methods: the linearized fluid approach and the Zeldovich approximation. We find that the free-particle approximation comprehensively out-performs both of these approximation schemes in all tests carried out and thus provides another useful analytical tool for studying structure formation on cosmological scales. 
C. J. Short and P. Coles (University of Nottingham, UK)