Jonathan L. Mace

Wave function confinement via transfer matrix methods

The exact transfer matrix approach used in studying sectionally constant potentials in one dimension is generalized to cylindrical and spherical geometries, where the potential depends only on radius. In each geometry two transfer matrices suffice to completely describe the wave function: one for handling a discontinuity in potential and one for handling a delta-function potential barrier. This method is then applied to the problem of confining a wave function in a cylindrical configuration using only a series of carefully placed delta function potential barriers. It is found that confinement can be made to increase nearly exponentially with the number of barriers if placed correctly, but that this arrangement has an exponentially sharp dependence on both barrier position and energy.

Outputs of Shock‐Loaded Small Piezoceramic Disks

Thin small‐diameter polycrystalline Lead‐Zirconate‐Titanate piezoceramic disks were shock loaded in the D33 orientation over a stress range of 0.1–30 GPa. Their electrical outputs were discharged into 50 Ω viewing resistors, producing typically 0.15 μs quasi‐triangular impulses ranging from 50–700 V. The gas gun flat plate impact approach and the high explosives (HE) plane wave lens approach were used to load piezoceramic elements. These piezoceramic elements consisted of 0.25 mm thick and 1.32 mm diameter disks that were ultrasonically machined from 25 mm piezocrystal disks of type APC 850, commercially produced by American Piezo Ceramic Inc. To facilitate our experiments, the piezoceramic elements were coaxially mounted at the tip of a 2.35 mm diameter brass tube, an arrangement that is commercialized by Dynasen, Inc. under the name Piezopin of model CA‐1136. Simple calculations on the electrical outputs produced by these piezoceramic disks reveal electrical outputs in excess of 3000 W. Such short burst...