Knowledge Bank

An asymptotic $method1$ previously used to derive explicit formulas for asymmetric rotor eigenvalues in the domain of high J and low K has been extended to the derivation of the corresponding formulas for various angular momentum operators of higher order. Such formulas should be useful in the theory of higher order centrifugal distortion effects in asymmetric rotor molecules, but might also be of interest in applications to some other problems. The method is based on the possibility of approximating matrices of the type encountered in the quantum mechanics of angular momentum by matrices generated by Mathieu-type differential equations. Asymptotic methods available in the theory of such differential equations are then used to derive asymptotic expansion formulas for the eigenvalues of the equations. These formulas approximate the desired matrix eigenvalues.