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Electrons do not pop out of a piece of copper lying on the table. Clearly, the “free” electrons in a metal are trapped inside the surface, at least at room temperature. In other words, there is a potential barrier at the surface that prevents electrons from escaping at ordinary temperatures. In a crystalline metallic solid, there are positive ions at the lattice sites. Due to the Coulomb
interaction, these positive ions give rise to an attractive potential energy for an electron. Of course, the electrons repel each other. The overall potential for a single electron within the metal is a superposition of the potentials due to the positive ions and the other electrons. A square-well potential is a useful first model for the net potential that an electron experiences. Electronelectron
interactions in many cases play a minor role because the mobile electrons tend to avoid each other due to the Pauli principle. Thus, each electron is essentially independent of the others, i.e., it is nearly free. The potential inside the metal due to the ion cores varies rapidly but “averages out” due to the motion of the electron to an approximately constant value. This is a first approximation for the treatment of electrons in metals.

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