On the Asymmetrical Top in Quantum Mechanics

摘要: An elaboration and a more complete analysis of Witmer's work on the asymmetrical top treated as perturbation symmetrical one show that can deduce rigorous solution problem from those algebraic equations degree $2j+1$ or less. Without actually solving such equations, we find terms divisible into even odd groups just in case sigma-type doubling diatomic molecules by Kronig, Van Vleck others. For where asymmetry is slight, an explicit expression for separation similar doublets obtained. The selection rules, which are any asymmetry, consist following: (a) Kronig's rule; (b) $\ensuremath{\Delta}j=0, \ifmmode\pm\else\textpm\fi{}1$; $\ensuremath{\Delta}m=0, (c) rule quantum number sigma, $\ensuremath{\Delta}\ensuremath{\sigma}=\mathrm{even}\mathrm{for}\mathrm{electric}\mathrm{moment}$ $z$ direction $\ensuremath{\Delta}\ensuremath{\sigma}=\mathrm{odd}\mathrm{for}\mathrm{moment}$ $x\ensuremath{-}y$ plane. effect electronic motions rotation polyatomic molecule whole also briefly discussed.