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Easy physics-inspired approximations of the total and binding energies for the H atom and for the molecular ions H2(+)(ppe), H3(2+)(pppe), (HeH)++(αpe), He2(3+)(ααe) as well as quadrupole moment for the H atom and the equilibrium distances of the molecular ions in strong magnetic fields > 109 G are proposed. The idea of approximation is based on the assumption that the dynamics of the one-electron Coulomb system in a strong magnetic field is governed by the ratio of transverse to longitudinaldoi:10.1135/cccc20051133 fatcat:225e4czgirh2xhqjwqwpdnxi5i