Quantum Motion of Hydrogen

The simplest model describing general features of hydrogen tunneling is that of a particle in a double-well potential (Eig. 26.9). If the positions of the two minima are close to each other, and the barrier between them is not too high, one may expect an overlap of the ground-state wavefunctions of a particle oscillating in 

If the double-well potential is characterized by the asymmetry e (see Fig. 26.9), the splitting of the ground state is given by 

the asymmetry of the potential leads to the increase in the splitting and to the partial localization of the particle in the minimum with lower energy. 

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Orlova N. D., Pozdniakova L. A. Profiles of infrared absorption bands and rotational motion of molecules in liquids. Quantum rotation of hydrogen-chloride molecules, Opt. Spectr. 35, 624-7 (1973). [Optika i Spectr. 35, 1074-7 (1973)]. 

S. Y. Kim and S. Hammes-Schiffer (2003) Molecular dynamics with quantum transitions for proton transfer Quantum treatment of hydrogen and donorac-ceptor motions. J. Chem. Phys. 119, pp. 4389-4398... 

Under these circumstances, the motion of this electron can be characterized using the adaptation of quantum model of hydrogen scaled as ... 

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

The first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

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