The Problem of the Normal Hydrogen Molecule in the New Quantum Mechanics

The solution of Schroedinger's equation for the normal hydrogen molecule is approximated by the function $C[e^{-\frac{z(r_1+p_2)}{a}}+e^{-\frac{z(r_2+p_1)}{a}}]$ where $a=\frac{h^2}{4{\pi }^{2}m{e}^2}$, $r_1$ and $p_1$ are the distances of one of the electrons to the two nuclei, and $r_2$ and $p_2$ those for the other electron. The value of $Z$ is so determined as to give a minimum value to the variational integral which generates Schroedinger's wave equation. This minimum value of the integral gives the approximate energy $E$. For every nuclear separation $D$, there is a $Z$ which gives the best approximation and a corresponding $E$. We thus obtain an approximate energy curve as a function of the separation. The minimum of this curve gives the following data for the configuration corresponding to the normal hydrogen molecule: the heat of dissociation = 3.76 volts, the moment of inertia $J_0=4.59\mathrm{}\times {10}^{-41\mathrm{}}$ gr. ${\mathrm{cm}}^2$, the nuclear vibrational frequency ${\nu }_0=4900\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$.