Toroidal configuration of the orbit of the electron of the hydrogen ...

This value is in confirmation with the result x 0 = 0.141 obtained by Heyl andHernquist [6] (see Discussion). On the other hand, x 0 is related in accord toEq. (3.28) to the intensity of the magnetic field,x 0 = 2z 0n = √8¯hcπn 2 eB , (3.33)from which we obtain B ≃ 4.7 · 10 12 Gauss. Hence, at this field intensitythe ground state energy of the hydrogen atom is given by E ′ = −1/(2n 2 ) =−15.58 Rydberg.0.80.6n=0.253, x0=0.141chi0.40.20-10 -5 0 5 10xFigure 7: The longitudinal ground state wave function χ(x), Eq. (3.34), ofthe hydrogen atom in the magnetic field B = 4.7 · 10 12 Gauss; n = 1/ √ −2E,x = 2z/n.The longitudinal ground state wave function is given byχ(x) ≃ (|x| + x 0 )e (|x|+x 0)/n U(1 − n, 2, |x| + x 0 ), (3.34)and is plotted in Fig. 7). The total wave function is√1χ(x) ≃ e − r24R 22πR02 0 (|x| + x 0 )e (|x|+x0)/n U(1 − n, 2, |x| + x 0 ), (3.35)and the associated three-dimensional probability density is schematically depictedin Fig. 8.In contrast to the double Landau-type orbit implied by the Coulombpotential approximation, the modified Coulomb potential approach provides21