We present a calculation of the charm and gluon fragmentation contributions to inclusive J/ψ and ψ ′ production at large transverse momentum at the Tevatron. For ψ production, we include both fragmentation directly into ψ and fragmentation into χ c followed by the radiative decay χ c → ψ+γ. We find that fragmentation overwhelms the leading-order mechanisms for prompt ψ production at large p T , and that the dominant contributions come from fragmentation into χ c . Our results are consistent with recent data on ψ production from the CDF and D0 experiments. In the case of prompt ψ ′ production, the dominant mechanism at large p T is charm fragmentation into ψ ′ . We find serious disagreement between our theoretical predictions and recent ψ ′ data from the Tevatron.

We discuss some of the properties of the 'collision' of a quantum mechanical wave packet with an infinitely high potential barrier, focusing on novel aspects such as the detailed time-dependence of the momentum-space probability density and the time variation of the uncertainty principle product ∆x t · ∆p t . We make explicit use of Gaussian-like wave packets in the analysis, but also comment on other general forms.

We calculate the Wigner quasi-probability distribution for position and momentum, P (n) W (x, p), for the energy eigenstates of the standard infinite well potential, using both x-and p-space stationary-state solutions, as well as visualizing the results. We then evaluate the time-dependent Wigner distribution, P W (x, p; t), for Gaussian wave packet solutions of this system, illustrating both the short-term semi-classical time dependence, as well as longer-term revival and fractional revival behavior and the structure during the collapsed state. This tool provides an excellent way of demonstrating the patterns of highly correlated Schrödinger-cat-like 'mini-packets' which appear at fractional multiples of the exact revival time.

We present quasi-analytical and numerical calculations of Gaussian wave packet solutions of the Schrödinger equation for two-dimensional infinite well and quantum billiard problems with equilateral triangle, square, and circular footprints. These cases correspond to N = 3, N = 4, and N → ∞ regular polygonal billiards and infinite wells, respectively. In each case the energy eigenvalues and wavefunctions are given in terms of familiar special functions. For the first two systems, we obtain closed form expressions for the expansion coefficients for localized Gaussian wavepackets in terms of the eigenstates of the particular geometry. For the circular case, we discuss numerical approaches. We use these results to discuss the short-time, quasi-classical evolution in these geometries and the structure of wave packet revivals. We also show how related half-well problems can be easily solved in each of the three cases.

We study the effects of noncommutative QED ͑NCQED͒ in fermion pair production, ␥ϩ␥→ f ϩ f, and Compton scattering, eϩ␥→eϩ␥. Non-commutative geometries appear naturally in the context of string or M theory and give rise to 3-and 4-point photon vertices and to momentum dependent phase factors in QED vertices which will have observable effects in high energy collisions. We consider e ϩ e Ϫ colliders with energies appropriate to the TeV linear collider proposals and the multi-TeV CLIC project operating in ␥␥ and e␥ modes. Noncommutative scales roughly equal to the center of mass energy of the e ϩ e Ϫ collider can be probed, with the exact value depending on the model parameters and experimental factors. However, we find that the Compton process is sensitive to ⌳ NC values roughly twice as large as those accessible to the pair production process.