Group theory applied to the hydrogen atom in a strong magnetic field. Derivation of the effective diamagnetic Hamiltonian

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Abstract
The authors present a formalism based on the non-invariance algebra for the Coulomb problems that allows one to deduce an effective Hamiltonian for a wide variety of perturbing potentials. Applications to the problem of the hydrogen atom in magnetic field are performed. They especially derive the exact first- and second-order expressions of the effective diamagnetic Hamiltonian under a general operator form. Some of the consequences and further developments are briefly indicated.