Resonant scattering and quasibound states with Airy functions

Resonant scattering and quasibound states in quantum mechanics are often introduced using constant-potential solutions of the time-independent Schrödinger equation. While perhaps the simplest approach, other solutions can also demonstrate these phenomena. In this paper, a one-dimensional linear potential with a jump discontinuity illustrates resonant and quasibound behavior in connection with the Airy functions. Resonances in the reflection probability can be induced in a mathematically simple way by incorporating absorption into the problem. The analysis focuses on the probability current and employs techniques at the undergraduate level.