In the field of quantum magnetism, neutron scattering techniques allows probing of the magnetic properties of many materials, as the neutrons carry spin. Interesting materials are for example the parent compound of a high temperature superconductor La2CuO4 or the band insulator Cu(DCOO)2·4D2O (known as CFTD). Although the electrical properties of these two compounds are different, both show antiferro-magnetic Heisenberg coupling of spin 1/2 in a 2D square lattice geometry, with very weak interplane coupling in the third direction, which implies that the magnetic properties of both La2CuO4 and CFTD present many similarities. In such systems, the excitations of the spins are known as spin waves, and neutron scattering has played a crucial part in better understanding this theory, as it gives the possibility to directly probe the correlation functions describing the system. However, the compounds have also been found to have non classical and highly fluctuating behaviour, due to the quantum nature of spin 1/2 spins and the low dimensionality antiferro-magnetic system.