Quantum Physics For Dummies, Revised Edition

Chapter 10

Handling Many Identical Particles

In This Chapter

Looking at wave functions and Hamiltonians in many-particle systems

Working with identical and distinguishable particles

Identifying and creating symmetric and antisymmetric wave functions

Explaining electron shells and the periodic table

Hydrogen atoms (see Chapter 9) involve only a proton and an electron, but all other atoms involve more electrons than that. So how do you deal with multiple-electron atoms? For that matter, how do you deal with multi-particle systems, such as even a simple gas?

In general, you can’t deal with problems like this — exactly, anyway. Imagine the complexity of just two electrons moving in a helium atom — you’d have to take into account the interaction of the electrons not only with the nucleus of the atom but also with each other — and that depends on their relative positions. So not only does the Hamiltonian have a term in 1/r1 for the potential energy of the first electron and 1/r2 for the second electron, but it also has a term in for the potential energy that comes from the interaction ...