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Lie Groups, Physics, and Geometry by Robert Gilmore

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14

Hydrogenic atoms

 

 

Many physical systems exhibit symmetry. When a symmetry exists it is possible to use group theory to simplify both the treatment and the understanding of the problem. Central two-body forces, such as the gravitational and Coulomb interactions, give rise to systems exhibiting spherical symmetry (two particles) or broken spherical symmetry (planetary systems). In this chapter we see how spherical symmetry has been used to probe the details of the hydrogen atom. We find a hierarchy of symmetries and symmetry groups. At the most obvious level is the geometric symmetry group, SO(3), which describes invariance under rotations. At a less obvious level is the dynamical symmetry group, SO(4), which accounts for the degeneracy ...

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