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In this paper, the modified hydrodynamic equations of a quantum system consisting of a degenerate electron gas and a classical ion gas, which take into account quantum shell effects, are derived. Two approaches are considered. The first is based on the modification of hydrodynamic equations. The modified equations take into account the shell effects by introducing an additional external field into the equations of motion for the electronic component. The second approach is based on a simplified description of the DFT modeling of the electron distribution for a given ionic distribution. In deriving the self-consistent system of equations, the Green’s function method is used in the coordinate representation, previously successfully applied in analyzing quantum shell effects in a gas bubble of submicron size.

Modified hydrodynamic equations of quantum liquid, taking into account quantum shell effects