How to scale the wave functions in a simple solvable model

Abstract

The scaling properties of the exact wave functions in the two-level pairing model are studied and a welldefined limit, when the number of pairs goes to infinity, is found. An approximate method for obtaining the scaled wave functions is discussed. Well-known methods for relating finite-difference equations with differential ones are used, together with a semiclassical expansion. The approximate results obtained agree well with the exact ones. A comparison with the time-dependent Hartree-Fock approach is also done.