Applications of density matrix in the fractional quantum mechanics: Thomas–Fermi model and Hohenberg–Kohn theorems revisited

The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas–Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg–Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.

► Thomas–Fermi model under the framework of fractional quantum mechanics is studied.
► We show the validity of the HK theorems in the space fractional quantum mechanics.
► The density functional theory is generalized to the fractional quantum mechanics.