Due to electrostatic repulsion the two electrons will repel each other as they both possess similar charges (lets leave gravitational attractive force out of the picture).
My question is: can there be any attractive force(s) between the electrons? I know the reason that the particles stated above cannot share the same quantum state is due to the Pauli Exclusion Principle (PEP).
Best Answer
you can check the discussion here. There is a certain case in which a phonon mediates attraction between two electrons. Indeed, acoustic phonons correspond to a slowly varying in-space displacement of atoms which produces a charge. This charge, in turn, results in an electric potential for the electrons. This means that the electron distorts the crystal lattice (builds up a positive charge around itself) which, at the end, attracts other electrons.