An accurate analytical wavefunction for circular Rydberg states of the H atom in a magnetic field

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Abstract
By performing first-order perturbation theory about the mod m mod to infinity limit, we obtain a highly accurate analytical expression for circular Rydberg ( mod m mod =n-1>>1) wavefunctions of the hydrogen atom in a uniform magnetic field. In the mod m mod to infinity limit, the electron executes a circular orbit about the magnetic field axis; the first-order wavefunction simply corresponds to Gaussian fluctuations about this orbit. To demonstrate the utility of the results derived here. We compare our simple expression for the lifetimes of mod m mod =25 and 35 circular states with accurate ab initio results.