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So the electromagnetic force holds matter together, but in a quantum mechanical way. As for metallic bonds I have no clue how that works. The idea seems to be that a sea of electrons acts as a glue that holds together an array of nucleons. Not sure how Schrodinger's equation gets you that.
The two forces that hold atoms together in a molecule are the electric force and the nuclear force. These forces bind the three parts of an atom, which include electrons, neutrons and protons. Continue Reading. Electrons, which have a negative charge, orbit the nucleus in an atom. Protons, which have a positive charge, are inside the nucleus. Because electrons and protons have opposite charges, the electric force causes them to pull toward one another. An atom usually contains the same number of electrons and protons.