[en] Fission is a complex process which highlights many nuclear properties. A major challenge in theoretical nuclear physics nowadays is the development of a consistent approach able to describe on the same footing the whole fission process, i.e. properties of the fissioning system, fission dynamics and fission fragment distributions. As a first step, a microscopic time-dependent and quantum mechanical formalism has been developed based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation. Pioneering results obtained for the low-energy fission of ²³⁸U encouraged us to perform new studies of fission along these lines with some additional improvements. For instance, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn't seem valid anymore, and intrinsic excitations have to be taken into account. For that purpose, a new theoretical framework called the Schroedinger Collective Intrinsic Model (SCIM) has been developed, which allows in a microscopic way a simultaneous coupling of single particle and collective degrees of freedom. Such an approach is based on a generalized Generator Coordinate Method (GCM), where the general GCM ansatz of the nuclear wave function is extended by a few excited configurations. Indeed, one considers as generating wave functions not only Hartree Fock Bogolyubov ground-state configurations with different values for the collective generator coordinate but also two quasi particle excited states. Such an approach has the advantage of describing in a completely quantum-mechanical fashion and without phenomenological parameters the coupling of quasi-particle degrees of freedom to the collective motion of the nucleons. In this talk, I will focus on the derivation of the newly developed SCIM formalism. I will first discuss the generalized Hill and Wheeler equation and its transformation into a non local Schroedinger equation by inverting the expansion of the overlap kernel. Then, I will present numerical results of the overlap kernel in a wide range of deformation in ²³⁶U. The final Schroedinger equation, written in a convenient form that has the advantage to exhibit typical terms occurring in the formalism will then be discussed. Finally, perspectives will be sketched