Z^2 in Schrodinger Equation
Posted: Sun Oct 20, 2019 5:52 pm
I'm confused by the books definition of trying to explain why Z^2 is more important than Z. The textbook says, "A skill to develop is to think about why a property depends on various parameters in a particular way. In this case you might wonder why the energy depends on Z 2 rather than on Z itself. The reason can be traced to two cooperating factors. First, a nucleus of atomic number Z and charge Ze gives rise to a field that is Z times stronger than that of a single proton. Second, the electron is drawn in by the higher charge and is Z times closer to the nucleus than it is in hydrogen. The two factors work together to give an overall energy lowering that is proportional to Z2." I don't understand the Z and Ze part of the first reason, and why the electron is Z times closer to the nucleus than if it were in a hydrogen.