Commit b7f293f0 authored by Joseph Weston's avatar Joseph Weston
Browse files

add aharanov-bohm image

parent dc159a4a
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Aharonov-Bohm effect"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<img src='images/aharonov-bohm.svg' width=40%/>\n",
"<small style=\"float:right;\">Image [CC-BY-SA-3.0](https://creativecommons.org/licenses/by-sa/3.0/deed.en), original by [Kismalac](https://commons.wikimedia.org/wiki/File:AharonovBohmEffect.svg)</small>"
]
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......@@ -2,10 +2,15 @@
# Aharonov-Bohm effect
%% Cell type:markdown id: tags:
<img src='images/aharonov-bohm.svg' width=40%/>
<small style="float:right;">Image [CC-BY-SA-3.0](https://creativecommons.org/licenses/by-sa/3.0/deed.en), original by [Kismalac](https://commons.wikimedia.org/wiki/File:AharonovBohmEffect.svg)</small>
%% Cell type:markdown id: tags:
In this tutorial, we are going to discuss one of the cornerstone of quantum nanoelectronics,
the Aharonov-Bohm effect. We are going to calculate the conductance of a ring through which one applies a magnetic field.
One interesting aspect of the Aharonov-Bohm effect is that the magnetic field can actually *vanish* in the sample itself. All that is required is that the potential vector does not. This is a very nice proof that in quantum mechanics the electron motion indeed couples to the potential vector, not the magnetic field. This can be seen from the following Gauge transformation: let us consider the Schrodinger equation $H\Psi = E\Psi$ with following Hamiltonian,
$$H = \frac{1}{2m} [ P - eA(R)]^2 + V(R)$$
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