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 for the potential energy of the first electron and for the second electron, but it also has a term in for the potential energy that comes from the interaction of the two electrons. And that makes an exact wave function just about impossible to find.

However, even without ...