V (r) = - kze? / r, (for r2 R). The total energy E of the...

 

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V (r) = - kze? / r, (for r2 R). The total energy E of the electron in a state y, is: (V) = j y, V y, dv Real nuclei are not points and the electron wave function can penetrate inside the nuclear charge distribution (r S R), for which the potential energy of the 1,r. - kZe? 3 electron is: V'(r) = R - 2 2 R The energy E' of the electron in a state of uniformly charged spherical nucleus is: (V") = [r<r WV' W, dv + S»r VnV Wn dv. %3D 2 kz*e?R? AE = E' - E = <V'> - <V> = 5 a V (r) = - kze? / r, (for r2 R). The total energy E of the electron in a state y, is: (V) = j y, V y, dv Real nuclei are not points and the electron wave function can penetrate inside the nuclear charge distribution (r S R), for which the potential energy of the 1,r. - kZe? 3 electron is: V'(r) = R - 2 2 R The energy E' of the electron in a state of uniformly charged spherical nucleus is: (V") = [r<r WV' W, dv + S»r VnV Wn dv. %3D 2 kz*e?R? AE = E' - E = <V'> - <V> = 5 a