Solution of time-dependent Schrodinger equation for field emission

Rutgers University, New Jersey, USA

September 27, 2018

In this talk, I will consider a metal in the presence of an electric field. I will mostly focus on the simple setting in which the electric field is constant (in space and time). In this case, the stationary solutions of the Schrodinger equation have been extensively studied, starting from a seminal paper by Fowler and Nordheim. I will consider the initial value problem, starting from a state in which the electrons in the metal are in a stationary state of the 0-field system. I will show that, at long times, the system evolves to the Fowler-Nordheim solution, and discuss some qualitative aspects of the transient regime. I will also discuss the more interesting situation of a (time-dependent) laser field.

Slides

PDF:

• Jauslin_Rutgers_2018.pdf

• tarball: 18rutgers-1.0.tar.gz
• git repository: 18rutgers-git (the git repository contains detailed information about the changes in the slides as well as the source code for all previous versions).

References

This presentation is based on

• [CCJL18]: Solution of the time dependent Schrodinger equation leading to Fowler-Nordheim field emission
  Ovidiu Costin, Rodica Costin, Ian Jauslin, Joel L. Lebowitz, 2018
  (published in Journal of Applied Physics, volume 124, number 213104, 2018)
  pdf, source