A Dirac delta function δ(x) barrier can be thought of as an infinitely high infinitesimally narrow spike at the origin. Although a classical particle cannot pass through such a barrier, quantum mechanics predicts a non-zero transmission probability. This simulation shows a quantum mechanical wave function Ψ(x,t) with energy eigenvalue E tunneling through a delta function barrier.
Griffiths Quantum Mechanics p76.
This simulation was created using the Easy Java Simulations (Ejs) modeling tool. You can modify this simulation if you have Ejs installed by right-clicking within a plot and selecting "Open Ejs Model" from the pop-up menu item. Information about Ejs is available at: < http://www.um.es/fem/Ejs/ >