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mlz
BornAgain
Commits
e7e22a38
Commit
e7e22a38
authored
1 year ago
by
Mikhail Svechnikov
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correct mu and epsilon
parent
3a977903
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1 merge request
!1661
DevRef 1.1 small fixes (#624)
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Doc/DevRef/Scattering.tex
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Doc/DevRef/Scattering.tex
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8 deletions
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8
−
8
View file @
e7e22a38
...
@@ -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\cdot
10
^{
-
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\cdot
10
^{
-
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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