Final Version of Note 177(4)

This is the final version of notes 177(4). In the 1s orbital of H there is a hitherto unknown, positive valued, repulsive, pure quantum force, eq. (11). At the point r = a where a is the Bohr radius, this quantum force exactly balances the classical force eq. (12), which is negative valued or attractive. This accounts for the stability of the 1s orbital, i.e. why the electron does not fall into the nucleus due to the attractive Coulombic force between electron and proton. The Bohr radius for 1s is the maximum value of the radial distribution function, Fig. (4.17), page 74, of P. W. Atkins, “Molecular Quantum Mechanics” (OUP, 2nd. ed., 1983). So the force eigenvalues can now be evaluated by computer algebra for the first few hydrogenic orbitals. These results emphasize that in the force equation of quantum mechanics:

(H hat – E) d psi / dx = F psi


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