Reviving Bohr Molecules

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Science  02 Sep 2005:
Vol. 309, Issue 5740, pp. 1459
DOI: 10.1126/science.309.5740.1459d

Before the Heisenberg-Schrödinger formulation of quantum mechanics, the semiclassical Bohr-Sommerfeld theory successfully accounted for quantized properties such as the energy levels in the hydrogen atom. However, the forcing of closed orbits for particle motion ran afoul of the uncertainty principle. Recently, the use of Dscaling, in which the motion of each particle is described by a vector in D dimensions, was used to reintroduce the uncertainty principle to this earlier theory. When properly done, such equations reduce to the correct Schrödinger form for D = 3 but can still be solved in the more tractable D→ ∞ limit. This D scaling approach was applied successfully to atoms but did not yield bound states for molecules.

Svidzinsky et al.have developed a D scaling description that fully quantizes one of the angles describing the interelectron coordinates and properly weights the contribution of electron-electron repulsion. After application of a leading correction term in 1/D, the potential energy curves for the lowest singlet, triplet, and excited states of H2 are in good agreement with accepted values after minimal numerical calculation. The procedure also yields reasonable agreement for the ground state of BeH. — PDS

Phys. Rev. Lett. 95, 080401 (2005).

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