Rovibrational spectroscopy calculations using a Weyl-Heisenberg wavelet basis and classical phase space truncation

New basis set methods are examined regarding quantum mechanical calculations of energy levels and wave functions of bound systems. The first method (I) involves compact orthogonal wavelets as the basis set which is subsequently truncated using the guidance of a classical phase space picture of the system. In this dissertation, the first application of this technique to a real molecular system (neon dimer) is presented, and many of the technical details are developed for its use on any arbitrary system. Although in many respects, neon dimer represents a "worst-case scenario" for the method, it is still competitive with another state-of-the-art scheme applied to the same system. The second method (II) greatly improves the computed accuracies of the first through the introduction of phase space region operators, which increase the efficiency K/N of the basis set, where N is the number of basis functions needed to calculate K energy eigenvalues to a given level of accuracy. For one model system, the absolute error of the computed energy levels is reduced by nearly 4 orders of magnitude, as compared to method I. Finally, a new parallel algorithm for matrix diagonalization (method III) is introduced, which uses a modified subspace iteration method. The new method exhibits great parallel scalability, making it possible to determine many thousands of accurate eigenvalues for sparse matrices of order N approximately N ~ 106 or larger.