Classical tunneling

Carl M. Bender, Daniel W. Hook

Classical mechanics is a singular theory in that real-energy classical particles can never enter classically forbidden regions. However, if one regulates classical mechanics by allowing the energy E of a particle to be complex, the particle exhibits quantum-like behavior: complex-energy classical particles can travel between classically allowed regions separated by potential barriers. When Im E → 0, the classical tunneling probabilities persist. Hence, one can interpret quantum tunneling as an anomaly. A numerical comparison of complex classical tunneling probabilities with quantum tunneling probabilities leads to the conjecture that as Re E increases, complex classical tunneling probabilities approach the corresponding quantum probabilities. Thus, this work attempts to generalize the Bohr correspondence principle from classically allowed to classically forbidden regions.

Er’el Granot

Resonant tunnelling (RT) is used as a pedagogical tool to emphasize the difference between quantum and classical physics. We calculate the RT reflection and transmission coefficients in both the classical and quantum scenarios, and RT is used to demonstrate the transition from the quantum domain to the classical one. We also use the classical result with a dimension analysis to derive the Landauer formula.

Ali Övgün

Thıs is my undergraduate thesis. So far I have worked on tunneling and its classi-cal, semi-classical and quantum description, then I looked some unsolved problems . Ihave learned about Hartman e ect , tunneling time, semi-classical approximations ,pathintegral and a classical description of tunneling

Alessandro Sist