Quantum Mechanics - Approximation Methods : Relativistic Correction and Fine Structure of H-Atom
As an application of stationary perturbation theory the energy correction for the hydrogen atom due to fine structure of hydrogen spectrum,has been calculated. The fine structure is due to two effects- spin-orbit coupling and the relativistic correction. In the previous video the energy correction due to the spin-orbit coupling had been calculated. Although the relativistic effect in hydrogen due to the motion of the electron is small, can still be detected spectroscopic techniques. Finding the perturbation Hamiltonian this correction has been furnished. It is found that the spin-orbit and relativistic corrections have the same order of magnitude 1/10^3ev. Fine structure correction is obtained by adding the expressions for the spin-orbit and relativistic corrections.