SF_SPIN

Description

SciFortan module for Pauli matrix algebra

Quick access

Variables:

pauli_0, pauli_1, pauli_2, pauli_3, pauli_sigma_0, pauli_sigma_1, pauli_sigma_2, pauli_sigma_3, pauli_sigma_minus, pauli_sigma_plus, pauli_sigma_x, pauli_sigma_y, pauli_sigma_z, pauli_tau_0, pauli_tau_1, pauli_tau_2, pauli_tau_3, pauli_tau_minus, pauli_tau_plus, pauli_tau_x, pauli_tau_y, pauli_tau_z, pauli_x, pauli_y, pauli_z, spin1_0, spin1_minus, spin1_plus, spin1_x, spin1_y, spin1_z, spin3half_0, spin3half_minus, spin3half_plus, spin3half_x, spin3half_y, spin3half_z

Variables

sf_spin/pauli_0

Pauli matrix 0 (2x2 identity) \(\sigma_0 = \begin{pmatrix}1&0\\0&1\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

reshape([one,zero,zero,one],[2,2])

sf_spin/pauli_1

\(\sigma_1 = \sigma_x\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x

sf_spin/pauli_2

\(\sigma_2 = \sigma_y\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_y

sf_spin/pauli_3

\(\sigma_3 = \sigma_z\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_z

sf_spin/pauli_sigma_0

\(\sigma_0 = \begin{pmatrix}1&0\\0&1\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_0

sf_spin/pauli_sigma_1

\(\sigma_1 = \sigma_x\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x

sf_spin/pauli_sigma_2

\(\sigma_2 = \sigma_y\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_y

sf_spin/pauli_sigma_3

\(\sigma_3 = \sigma_z\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_z

sf_spin/pauli_sigma_minus

2 x lowering operator \(\sigma_- = \sigma_x - i \sigma_y = \begin{pmatrix}0&0\\2&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x-xi*pauli_y

sf_spin/pauli_sigma_plus

2 x raising operator \(\sigma_+ = \sigma_x + i \sigma_y = \begin{pmatrix}0&2\\0&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x+xi*pauli_y

sf_spin/pauli_sigma_x

\(\sigma_x = \begin{pmatrix}0&1\\1&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x

sf_spin/pauli_sigma_y

\(\sigma_y = \begin{pmatrix}0&-i\\i&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_y

sf_spin/pauli_sigma_z

\(\sigma_z = \begin{pmatrix}1&0\\0&-1\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_z

sf_spin/pauli_tau_0

\(\tau_0 = \sigma_0\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_0

sf_spin/pauli_tau_1

\(\tau_1 = \sigma_x\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x

sf_spin/pauli_tau_2

\(\tau_2 = \sigma_y\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_y

sf_spin/pauli_tau_3

\(\tau_3 = \sigma_z\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_z

sf_spin/pauli_tau_minus

2 x lowering operator \(\tau_- = \tau_x - i \tau_y = \begin{pmatrix}0&0\\2&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x-xi*pauli_y

sf_spin/pauli_tau_plus

2 x raising operator \(\tau_+ = \tau_x + i \tau_y = \begin{pmatrix}0&2\\0&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x+xi*pauli_y

sf_spin/pauli_tau_x

\(\tau_x = \sigma_x\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_x

sf_spin/pauli_tau_y

\(\tau_y = \sigma_y\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_y

sf_spin/pauli_tau_z

\(\tau_z = \sigma_z\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

pauli_z

sf_spin/pauli_x

Pauli matrix x \(\sigma_x = \begin{pmatrix}0&1\\1&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

reshape([zero,one,one,zero],[2,2])

sf_spin/pauli_y

Pauli matrix y \(\sigma_y = \begin{pmatrix}0&-i\\i&0\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

reshape([zero,xi,-xi,zero],[2,2])

sf_spin/pauli_z

Pauli matrix z \(\sigma_z = \begin{pmatrix}1&0\\0&-1\end{pmatrix}\)

Type:

complex(2, 2)

Attributes:

public, parameter

Default:

reshape([one,zero,zero,-one],[2,2])

sf_spin/spin1_0

3x3 identity matrix \(\mathbb{1}_3 = \begin{pmatrix}1&0&0\\0&1&0\\0&0&1\end{pmatrix}\)

Type:

complex(3, 3)

Attributes:

public, parameter

Default:

reshape([one ,zero,zero,zero, one,zero,zero,zero,one],[3,3])

sf_spin/spin1_minus

spin 1 lowering operator \(S_- = S_x - i S_y = \sqrt{2}\begin{pmatrix}0&0&0\\1&0&0\\0&1&0\end{pmatrix}\)

Type:

complex(3, 3)

Attributes:

public, parameter

Default:

spin1_x-xi*spin1_y

sf_spin/spin1_plus

spin 1 raising operator \(S_+ = S_x + i S_y = \sqrt{2}\begin{pmatrix}0&1&0\\0&0&1\\0&0&0\end{pmatrix}\)

Type:

complex(3, 3)

Attributes:

public, parameter

Default:

spin1_x+xi*spin1_y

sf_spin/spin1_x

spin 1 matrix \(S_x\), basis m=1,0,-1 \(S_x = \frac{1}{\sqrt{2}}\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}\)

Type:

complex(3, 3)

Attributes:

public, parameter

Default:

reshape([zero, one,zero,one ,zero, one,zero, one,zero],[3,3])/sqrt2

sf_spin/spin1_y

spin 1 matrix \(S_y\), basis m=1,0,-1 \(S_y = \frac{1}{\sqrt{2}}\begin{pmatrix}0&-i&0\\i&0&-i\\0&i&0\end{pmatrix}\)

Type:

complex(3, 3)

Attributes:

public, parameter

Default:

reshape([zero,-xi ,zero,xi,zero ,-xi,zero,xi,zero],[3,3])/sqrt2

sf_spin/spin1_z

spin 1 matrix \(S_z\), basis m=1,0,-1 \(S_z = \begin{pmatrix}1&0&0\\0&0&0\\0&0&-1\end{pmatrix}\)

Type:

complex(3, 3)

Attributes:

public, parameter

Default:

reshape([one ,zero,zero,zero,zero,zero,zero,zero,-one],[3,3])

sf_spin/spin3half_0

4x4 identity matrix \(\mathbb{1}_4 = \begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}\)

Type:

complex(4, 4)

Attributes:

public, parameter

Default:

reshape([one,zero,zero,zero,zero,one,zero,zero,zero,zero,one,zero,zero,zero,zero,one],[4,4])

sf_spin/spin3half_minus

spin 3/2 lowering operator \(S_- = S_x - i S_y = \begin{pmatrix}0&0&0&0\\\sqrt{3}&0&0&0\\0&2&0&0\\0&0&\sqrt{3}&0\end{pmatrix}\)

Type:

complex(4, 4)

Attributes:

public, parameter

Default:

spin3half_x-xi*spin3half_y

sf_spin/spin3half_plus

spin 3/2 raising operator \(S_+ = S_x + i S_y = \begin{pmatrix}0&\sqrt{3}&0&0\\0&0&2&0\\0&0&0&\sqrt{3}\\0&0&0&0\end{pmatrix}\)

Type:

complex(4, 4)

Attributes:

public, parameter

Default:

spin3half_x+xi*spin3half_y

sf_spin/spin3half_x

spin 3/2 matrix \(S_x\), basis m=3/2,…,-3/2 \(S_x = \frac{1}{2}\begin{pmatrix}0&\sqrt{3}&0&0\\\sqrt{3}&0&2&0\\0&2&0&\sqrt{3}\\0&0&\sqrt{3}&0\end{pmatrix}\)

Type:

complex(4, 4)

Attributes:

public, parameter

Default:

reshape([zero ,s3 , zero , zero ,s3, zero, two, zero ,zero , two , zero , s3,zero , zero,s3, zero],[4,4])/2d0

sf_spin/spin3half_y

spin 3/2 matrix \(S_y\), basis m=3/2,…,-3/2 \(S_y = \frac{1}{2}\begin{pmatrix}0&-i\sqrt{3}&0&0\\i\sqrt{3}&0&-2i&0\\0&2i&0&-i\sqrt{3}\\0&0&i\sqrt{3}&0\end{pmatrix}\)

Type:

complex(4, 4)

Attributes:

public, parameter

Default:

reshape([zero ,-c3 , zero , zero ,c3, zero,-c2, zero ,zero ,c2 , zero ,-c3,zero , zero, c3, zero],[4,4])/2d0

sf_spin/spin3half_z

spin 3/2 matrix \(S_z\), basis m=3/2,…,-3/2 \(S_z = \frac{1}{2}\begin{pmatrix}3&0&0&0\\0&1&0&0\\0&0&-1&0\\0&0&0&-3\end{pmatrix}\)

Type:

complex(4, 4)

Attributes:

public, parameter

Default:

reshape([h32,zero,zero,zero,zero,h12,zero,zero,zero,zero,-h12,zero,zero,zero,zero,-h32],[4,4])