Sponsored by the Rutgers University Department of Mathematics and the

Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)

**Co-organizers:****Andrew Baxter**, Rutgers University, baxter{at} math [dot] rutgers [dot] edu**Doron Zeilberger**, Rutgers University, zeilberg {at} math [dot] rutgers [dot] edu

Title: Paradoxical Reflection, or Anti-Tunneling, in Quantum Mechanics

Speaker: **Roderich Tumulka**, Rutgers University

Date: Thursday, January 29, 2009 5:00pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

Abstract:

According to the tunnel effect of quantum mechanics, a quantum particle (of rather sharp energy E, and for simplicity in 1 dimension) may have positive probability to cross a barrier that would be impossible to cross for a classical particle of the same energy E. I'm talking about a similar phenomenon that even many researchers in mathematical physics were unwilling to believe: A quantum particle can be reflected when arriving at a sudden drop in potential. A classical particle would not do that, as the force points in the direction of motion and would thus accelerate the particle. As a consequence of this "paradoxical reflection," a particle can be imprisoned between two such potential cliffs---that is, on a plateau. Even though the particle has zero probability to stay on top forever, we could show that it has significant probability to stay on top much longer than classical mechanics would permit. This is joint work with Pedro Garrido (Spain), Sheldon Goldstein (Rutgers) and Jani Lukkarinen (Finland). The talk will not require prior knowledge of quantum mechanics.