Ian Jauslin

## Solution of the time dependent Schrodinger equation leading to Fowler-Nordheim field emission

2018

### Abstract

We solve the time-dependent Schrodinger equation describing the emission of electrons from a metal surface by an external electric field $E$, turned on at $t=0$. Starting with a wave function $\psi(x,0)$, representing a generalized eigenfunction when $E=0$, we find $\psi(x,t)$ and show that it approaches, as $t\to\infty$, the Fowler-Nordheim tunneling wavefunction $\psi_E$. The deviation of $\psi$ from $\psi_E$ decays asymptotically as a power law $t^{-\frac32}$. The time scales involved for typical metals and fields of several V/nm are of the order of femtoseconds. We plot the short-time evolution of the current and density.

PDF:

LaTeX source:
• tarball: 18ccjl-1.1.tar.gz
• git repository: 18ccjl-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).

### Talks

This work has been presented at the following conferences:

• [GT19]: Field electron emission and the Fowler-Nordheim equation
GeorgiaTech, Atlanta, Georgia, USA, Feb 22 2019
pdf, source

• [Pr18b]: Field electron emission and the Fowler-Nordheim equation
Princeton University, New Jersey, USA, Nov 13 2018
pdf, source

• [Rut18]: Solution of time-dependent Schrodinger equation for field emission
Rutgers University, New Jersey, USA, Sep 27 2018
pdf, source

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