This thesis explores cosmological structure formation through the Schr¨odinger- Poisson (SP) framework, building on the foundational work of Widrow and Kaiser [3]. By treating dark matter as a wave-like field, the SP formalism provides a novel perspective that addresses challenges in traditional approaches, such as the Zel’dovich approximation’s (ZA) failure in nonlinear regimes. The main contributions of this work lie in advancing theoretical understanding, developing computational techniques, and applying the SP framework to foundational models of cosmic evolution. The thesis begins by outlining the limitations of the standard ΛCDM paradigm and establishes the SP system as an alternative framework. A detailed study of cosmic voids demonstrates the SP method’s ability to model void expansion beyond shell-crossing, naturally accommodating multistreaming regions using wave interference effects. These features circumvent the unphysical predictions of particle-based and traditional fluid models. A key innovation introduced in this thesis is the exploration of viscosity within the SP framework, resulting in a novel scaling solution analogous to the Reynolds number in classical fluid dynamics. This insight enriches our understanding of how small-scale quantum effects influence large-scale structure formation. Furthermore, the SP formalism is evaluated as a reconstruction tool for cosmological initial conditions. Preliminary results show its potential to outperform standard methods in certain scenarios, particularly in simplified power-law universes, while maintaining competitive accuracy in ΛCDM contexts. The findings underscore the versatility of the SP approach, not only as a theoretical tool for understanding dark matter dynamics but also as a practical method for reconstructing initial conditions and analysing observational data. The thesis concludes by highlighting potential applications, including filament dynamics, redshift-space reconstructions, and the integration of SP into future observational pipelines, particularly in the context of upcoming surveys like Euclid and DESI. Through its contributions, this thesis advances both theoretical and computational cosmology, demonstrating the promise of the Schr¨odinger-Poisson framework as a powerful tool for exploring the complex dynamics of the universe.