From 6413c2959cee0a1126589b46ea57c2bf52297c30 Mon Sep 17 00:00:00 2001
From: Joseph Weston <joseph@weston.cloud>
Date: Fri, 5 Jul 2019 12:07:36 +0200
Subject: [PATCH] whitespace fix
---
doc/source/tutorial/magnetic_field.rst | 16 ++++++++--------
1 file changed, 8 insertions(+), 8 deletions(-)
diff --git a/doc/source/tutorial/magnetic_field.rst b/doc/source/tutorial/magnetic_field.rst
index 6bb6fdcd..5bf242e7 100644
--- a/doc/source/tutorial/magnetic_field.rst
+++ b/doc/source/tutorial/magnetic_field.rst
@@ -37,7 +37,7 @@ The eigenstates satisfy :math:`a^\dagger a | n \rangle = n | n \rangle` with the
Landau level index :math:`n \geq 0`, and in coordinate representation are proportional to
.. math::
-
+
\psi_n (x, y) = \left( \frac{\partial}{ \partial w} - \frac{w^*}{4 l_B^2} \right)
w^n e^{-|w|^2/4l_B^2},
@@ -47,7 +47,7 @@ with :math:`w = x + i y`. The matrix elements of the ladder operators are
\langle n | a | m \rangle = \sqrt{m}~\delta_{n, m-1}, \quad \quad
\langle n | a^\dagger | m \rangle = \sqrt{m + 1}~\delta_{n, m+1}.
-
+
Truncating the basis to the first :math:`N` Landau levels allows us to approximate
the Hamiltonian as a discrete, finite matrix.
@@ -56,16 +56,16 @@ We can now formulate the algorithm that Kwant uses to compute Landau levels.
1. We take a generic continuum Hamiltonian, written in terms of the kinetic
momentum :math:`\vec{k}`. The Hamiltonian must be translationally
invariant along the directions perpendicular to the field direction.
-
+
2. We substitute the momenta perpendicular to the magnetic field with the ladder
operators :math:`a` and :math:`a^\dagger`.
-
+
3. We construct a `kwant.builder.Builder` using a special lattice which includes
the Landau level index :math:`n` as a degree of freedom on each site. The directions
normal to the field direction are not included in the builder, because they are
encoded in the Landau level index.
-
-This procedure is automated with `kwant.continuum.discretize_landau`.
+
+This procedure is automated with `kwant.continuum.discretize_landau`.
As an example, let us take the Bernevig-Hughes-Zhang model that we first considered in the
discretizer tutorial ":ref:`discretize-bhz-model`":
@@ -155,7 +155,7 @@ with the Landau levels shown as dashed lines.
h = landau_syst.hamiltonian_submatrix(params=params)
for ev in scipy.linalg.eigvals(h):
ax.axhline(ev, linestyle='--')
-
+
The dispersion and the Landau levels diverge with increasing energy, because the real space
discretization of the ribbon gives a worse approximation to the dispersion at higher energies.
@@ -229,4 +229,4 @@ to construct our heterostructure:
.. rubric:: Footnotes
.. [#] `Wikipedia <https://en.wikipedia.org/wiki/Landau_quantization>`_ has
- a nice introduction to Landau quantization.
\ No newline at end of file
+ a nice introduction to Landau quantization.
--
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