Bruce R. Johnson

Metallic nanoparticles are known to dramatically modify the spontaneous emission of nearby fluorescent molecules and materials. Here we examine the role of the nanoparticle plasmon resonance energy and nanoparticle scattering cross section on the fluorescence enhancement of adjacent indocyanine green (ICG) dye molecules. We find that enhancement of the molecular fluorescence by more than a factor of 50 can be achieved for ICG next to a nanoparticle with a large scattering cross section and a plasmon resonance frequency corresponding to the emission frequency of the molecule.

Two new numerical methods, the log derivative and the renormalized Numerov, are developed and applied to the calculation of bound-state solutions of the one-dimensional Schroedinger equation. They are efficient and stable; no convergence difficulties are encountered with double minimum potentials. A useful interpolation formula for calculating eigenfunctions at nongrid points is also derived. Results of example calculations are presented and discussed.

Exact quantum-mechanical calculations of the transition probabilities for the collinear collision of an atom with a diatomic molecule are performed. The diatomic molecule is treated as a harmonic oscillator. A range of interaction potentials from very hard to very soft are considered. It is found that for ``realistic'' interaction potentials the approximate calculations of Jackson and Mott are consistently high, even when the transition probabilities are low and good approximate results are expected. In some cases double and even triple quantum jumps are more important than single quantum jumps. Comparisons are made with exact classical calculations. A semiempirical formula is given for computing quantum-mechanical transition probabilities from classical calculations.

The renormalized Numerov method, which was recently developed and applied to the one-dimensional bound state problem [B. R. Johnson, J. Chem. Phys. 67, 4086 (1977)], has been generalized to compute bound states of the coupled-channel Schroedinger equation. Included in this presentation is a generalization of the concept of a wavefunction node and a method for detecting these nodes. By utilizing node count information it is possible to converge to any specific eigenvalue without the need of an initial close guess and also to calculate degenerate eigenvalues and determine their degree of degeneracy. A useful interpolation formula for calculating the eigenfunctions at nongrid points is also given. Results of example calculations are presented and discussed. One of the example problems is the single center expansion calculation of the 1sσg and 2sσg states of H+2.