Particle in Three Dimensions

Abstract

Many concepts introduced in the study of a particle in one dimension can be adapted directly to the particle in three dimensions. Angular momentum operators, however, are new. Closely linked with the particle in three dimensions, they are much like the spin operators we examined in Chap. 4. Angular momentun operators are particularly useful where the potential is spherically symmetric. They help in partially solving the problem of the Hamiltonian’s eigenvalues and eigenfunctions. For the r ^-1 and the spherical well potential, a complete solution is obtained. Electrically charged, a particle in three dimensions will interact with an external electromagnetic field. That interaction is responsible for the existence of atoms and molecules.