The old problem of the discrete spectrum of the hydrogen atom obeys a SO(4) symmetry, which is isomorphous to two subgroups that obey the algebra of angular momentum. The algebraic structure allows us to formulate a basis closely related to the properties of the wave function in parabolic coordinates. On the other hand, the properties of other angular momenta, such as electron spin and nucleus spin, are introduced by adding angular momentum. All these contributions are known as the hyperfine structure. In this work, we explore the symmetries of the problem to analyze the atomic hyperfine structure strictly using the properties of the SO(4) group of the Laplace-Runge-Lenz vector. Additionally, we have done a brief analysis of the symmetry breaking in the presence of electric and magnetic fields.
|Presenter name||Freddy Jackson Poveda Cuevas|
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