Exact Results in Quantum Theory

Studies on exchange energy in the hydrogen molecule reach back to the early days of quantum mechanics. Although the non-relativistic system itself and the formulation of the problem appear relatively simple, its long-range asymptotics still raises controversy, primarily due to cumbersome electron correlation effects and near singular wavefunction in the proximity of internuclear axis. I will present and discuss high-precision variational calculations of energy splitting between the lowest singlet and triplet states in the hydrogen molecule. Owing to explicitly correlated exponential basis employed in the calculations, we claim that due to its correct asymptotic behaviour our numerical results resolve the controversy of functional asymptotic form of exchange energy in H2.