abstract
- Editor's Note: Analyzing the one-dimensional Dirac delta-function potential is a rite of passage in quantum mechanics. Its bound state energy and reflection and transmission coefficients are familiar to most physicists. But what about the higher-dimensional analogs of the familiar spike in one dimension: a two-dimensional Dirac ring or a three-dimensional Dirac bubble? In this paper, the authors derive the bound state spectrum as well as the transmission and reflection coefficients for these potentials to reveal similarities and surprising differences in the behavior of particles in one, two, and three dimensions. The analysis is suitable for an undergraduate or graduate quantum mechanics course, adding two more exactly solvable potentials for the quantum canon. The calculations also provide interesting application of Bessel functions and spherical harmonics that could augment courses in mathematical methods. © 2025 Author(s).