Quantum Reflectionless Potential Well Explorer

Live Script exploring reflectionless potential wells through numerical integration of the Schrödinger equation.

This educational Live Script explores the transmission of wave packets by attractive hyperbolic Pöschl–Teller potentials through numerical integration of the Schrödinger equation in two dimensions. Remarkably, these potentials are exactly solvable and reflectionless - any incident wave has unit transmission probability. The script uses a sixth-order approximation to represent spatial derivatives and illustrates matrix exponential time evolution. The motion of the wave packet centroid is compared to the classical motion.

The script may interest students and instructors of physics and related fields. 'Try this' suggestions and some challenges along with references are included for further exploration. Additional related Live Scripts by the author are available at the MathWorks File Exchange.