What is the electron density?

Although the electron density can be calculated with the formal resources of quantum mechanics, in physics it does not play the leading role that the quantum state does. In contrast, the concept of electron density is central in quantum chemistry. There is no doubt about how the electron density is computed in terms of the wave function of an atom or molecule. However, when the interpretation of the concept is at stake, there is no general agreement. In this article we will analyze the two main interpretations of the concept of electron density: the Born-style probability density interpretation and the Schrödinger-style charge density interpretation. In particular, we will examine their differences, their relations with quantum mechanics and the consequences that each of them entails from a strictly quantum point of view.