Development and application of large-N expansions to problems in quantum mechanics and an investigation of the leading particle effect

We apply large-N approximation methods, where N is the number of spatial dimensions, to various problems in quantum mechanics. Specifically we investigate the application of the shifted and unshifted 1/N expansions to one dimensional symmetric potentials. In most cases we obtain fast and accurate results for both the energy eigenvalues and wave functions for a wide variety of potentials. In addition, the first systematic large-N expansions for quantities of interest in non-relativistic quantum scattering theory is presented. The formalism, valid for spherically symmetric potentials, is applied in calculations of the scattering lengths and phase shifts of various potentials in N = 3 dimensions. The results, complete to three orders in the large-N series, are in excellent agreement with numerical results for potentials strong enough to hold at most one bound state. Our approach is motivated by some recent work which shows how scattering from the exactly solvable delta-shell potential can be chosen as the large-N unperturbed problem. Finally we investigate the leading particle effect in high energy physics. We suggest that the leading particle effect directly reflects the amount of disruption suffered by the incident hadron in a collision. We make some simple models and examine the consequences. Under suitable circumstances a forward peak is predicted in certain nondiffractive interactions