Wavelet Solution of the Molecular Schrodinger Equation

布鲁斯河莱斯大学的约翰逊得到了化学系理论和计算化学项目的一个奖项的支持，该奖项将在分子量子力学中开发和应用多尺度小波方法。具体目标集中在分子薛定谔方程的解决方案，激发需要大振幅的振动运动的特点探测在解离共振拉曼光谱。在1-D开发的小波传播方法被带到3-D在全小波应用亚硝酰氯光激发在A波段。这是使通过使用旧的和新派生的多小波（适合在一个区间内）作为扩展基地的曲线雅可比坐标和时间。这项工作是固有的兴趣，了解拉曼光谱的ClNO，但也将作为一个测试床，进一步发展的适应性的方法。随后的工作将包括推动推广小波传播方法，以与显式时间依赖的哈密顿算子一起使用。正在开发一个计算机程序MultiWavePack，将常用的小波工具组装成一个免费提供的软件包。进一步的小波工作包括时域电动力学求解器和模型晶体的Wannier函数渐近行为的数值研究。PI还负责监督应用物理博士。计划和本科生的研究经验（REU）网站作为水稻量子研究所的执行主任。

Bruce R. Johnson of Rice University is supported by an award from the Theoretical and Computational Chemistry program within the Division of Chemistry for research which will develop and apply multiscale wavelet methods in molecular quantum mechanics. Specific goals are centered on the solution of the molecular Schrodinger equation, motivated by the need for large amplitude descriptions of the vibrational motion characteristically probed in dissociative resonance Raman spectroscopy. A wavelet propagation method developed in 1-D is being brought to 3-D in an all-wavelet application for nitrosyl chloride photoexcited in the A band. This is enabled by use of older and newly derived multiwavelets (adapted to fit within an interval) as expansion bases for both curvilinear Jacobi coordinates and time. This work is of intrinsic interest for understanding the Raman spectroscopy of ClNO, but will also serve as a test bed for further development of adaptivity of the method. Subsequent work will include a push to generalize the wavelet propagation method to use with Hamiltonians that are explicitly time-dependent. A computer program MultiWavePack is under development to assemble the frequently used wavelet tools into one freely available package. Further wavelet work proposed includes time domain electrodynamic solvers and numerical investigation of Wannier function asymptotic behavior for model crystals. The PI also oversees the Applied Physics Ph.D. program and a Research Experiences for Undergraduates (REU) site as Executive Director of the Rice Quantum Institute.