Wigner’s jellium is a theoretical model that describes a gas composed of electrons.In this concept, the overall charge is neutralised by n particles, each with a negativeunit charge, floating in a medium of uniformly distributed positive charges. The interactionsbetween the particles are dictated by the Coulomb potential. In this thesis, the Maxwell-Boltzmann distribution is used to describe the statistical behaviour of the quantum jelliummodel in a one-dimensional environment. We state a process-level large deviation principlefor the empirical field and prove it using similar techniques as done by Hirsch, Jansen and Jung (2022).