Exact motion in noncentral electric fields

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Abstract
We study the problem of the motion of a charged particle in noncentral potentials of the type f(θ)/r2 + V(r). Newton's and Schrödinger's mechanics are considered. Exact solutions exist if V(r)=−H/r or Kr2 (i.e., Coulomb or harmonic oscillator potentials) while f(θ) may have at least three different expressions as a function of θ if the problem is three‐dimensional and seven expressions if it is two‐dimensional. The classical trajectories are computed and the energy levels in the corresponding quantum problem are given. Analogies between the two treatments are discussed.