Asymptotics and Numerical Approaches to Quantum Mechanical Problems of Multidimensional Atomic and Molecular Systems

Asymptotic and numerical analyses in the multidimensional phase space of quantum and molecular systems are presented. The asymptotics of the Shannon information entropy for high-energy states and increasing spatial dimensionality are addressed. D-Dimensional hydrogenic atoms and harmonic oscillators serve as examples of multidimensional quantum systems. For the dynamics of weakly coupled atomic and molecular systems, the numerical effective mode method is explained, and its application to water molecular clusters is discussed.