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Commit e7e22a38 authored by Mikhail Svechnikov's avatar Mikhail Svechnikov
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correct mu and epsilon

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1 merge request!1661DevRef 1.1 small fixes (#624)
...@@ -259,7 +259,7 @@ the propagation of free neutrons becomes spin dependent. ...@@ -259,7 +259,7 @@ the propagation of free neutrons becomes spin dependent.
Therefore the scalar wavefunction of \cref{SnScalar} Therefore the scalar wavefunction of \cref{SnScalar}
must be replaced by spinor $\v\Psi$. must be replaced by spinor $\v\Psi$.
\index{Spinor}% \index{Spinor}%
The magnetic moment~$\mu$ of the neutron The magnetic moment~$\mu_n$ of the neutron
\nomenclature[1μ024 2n000]{$\mu_\text{n}$}{Magnetic moment of the neutron} \nomenclature[1μ024 2n000]{$\mu_\text{n}$}{Magnetic moment of the neutron}
\index{Neutron!magnetic moment}% \index{Neutron!magnetic moment}%
\index{Magnetic moment!neutron}% \index{Magnetic moment!neutron}%
...@@ -271,15 +271,11 @@ With the coupling term, the Schrödinger equation~\cref{ESchrodi1} ...@@ -271,15 +271,11 @@ With the coupling term, the Schrödinger equation~\cref{ESchrodi1}
becomes becomes
\begin{equation}\label{EHSchrodi} \begin{equation}\label{EHSchrodi}
\left\{-\frac{\hbar^2}{2m}\Nabla^2+V(\r) \left\{-\frac{\hbar^2}{2m}\Nabla^2+V(\r)
+\mu\v{B}(\r)\bm{\hat\sigma}-\hbar\omega\right\} +\mu_n\v{B}(\r)\bm{\hat\sigma}-\hbar\omega\right\}
\v\Psi(\r) = 0, \v\Psi(\r) = 0,
\end{equation} \end{equation}
\nomenclature[1ψ150 2r040]{$\v\Psi(\r)$}{Stationary coherent spinor wavefunction}% \nomenclature[1ψ150 2r040]{$\v\Psi(\r)$}{Stationary coherent spinor wavefunction}%
where $\mu_0$ is the vacuum permeability, where ${\bm{\hat\sigma}}$ is the Pauli vector, composed of the three Pauli matrices.
\nomenclature[1μ024 00]{$\mu_0$}{Vacuum permeability, $4\pi\cdot10^{-7}$ Vs/Am}%
\index{Permeability}%
\index{Magnetic permeability}%
and ${\bm{\hat\sigma}}$ is the Pauli vector, composed of the three Pauli matrices.
\nomenclature[1σ04]{$\bm\sigma$}{Pauli \nomenclature[1σ04]{$\bm\sigma$}{Pauli
vector, composed of the three Pauli matrices: $\bm\sigma=(\sigma_x,\sigma_y,\sigma_z)$}% vector, composed of the three Pauli matrices: $\bm\sigma=(\sigma_x,\sigma_y,\sigma_z)$}%
\index{Pauli vector}% \index{Pauli vector}%
...@@ -291,6 +287,10 @@ We introduce the reduced field ...@@ -291,6 +287,10 @@ We introduce the reduced field
\nomenclature[2h050 2r040]{$\v{b}(\r)$}{Rescaled \nomenclature[2h050 2r040]{$\v{b}(\r)$}{Rescaled
field $\v{b}=(m\mu/2\pi\hbar^2)\v{B}$}% field $\v{b}=(m\mu/2\pi\hbar^2)\v{B}$}%
\index{Magnetizing field!reduced}% \index{Magnetizing field!reduced}%
where $\mu_0$ is the vacuum permeability,
\nomenclature[1μ024 00]{$\mu_0$}{Vacuum permeability, $4\pi\cdot10^{-7}$ Vs/Am}%
\index{Permeability}%
\index{Magnetic permeability}%
to rewrite the Schrödinger equation in analogy to~\cref{ESchrodi2} as to rewrite the Schrödinger equation in analogy to~\cref{ESchrodi2} as
\index{Schrodinger@Schrödinger equation!macroscopic}% \index{Schrodinger@Schrödinger equation!macroscopic}%
\begin{equation}\label{ESchrodi2H} \begin{equation}\label{ESchrodi2H}
...@@ -440,7 +440,7 @@ the time average is ...@@ -440,7 +440,7 @@ the time average is
\braket{\v S} = \frac{1}{4}\braket{\v E(\r) \times \v H(\r)^* + \text{c.~c.}}. \braket{\v S} = \frac{1}{4}\braket{\v E(\r) \times \v H(\r)^* + \text{c.~c.}}.
\end{equation} \end{equation}
\nomenclature[2c000 2c000]{$\text{c.~c.}$}{Complex conjugate}% \nomenclature[2c000 2c000]{$\text{c.~c.}$}{Complex conjugate}%
We specialize to vacuum with $\TENS\mu(\r)=1$ and $\TENS\eps(\r)=1$, We specialize to vacuum with $\TENS\eps(\r)=1$,
and obtain and obtain
\begin{equation} \begin{equation}
\braket{\v S} \braket{\v S}
......
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