momentum_matrix_elements{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculate polarization dependent momentum matrix elements \(\epsilon\cdot\langle \psi_i | \hat{\mathbf{p}} | \psi_j \rangle\) for wave functions within one band. The light polarization direction \(\epsilon\) is automatically normalized in the program.

For further reading: J. H. Davies, The Physics of Low-Dimensional Semiconductors. An Introduction, 2006, Chapters 10 and 8.

Nested keywords

name

Calling sequence

quantum{ region{ momentum_matrix_elements{ name = ... } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • type: character string

Functionality

defines suffix for related output files

direction

Calling sequence

quantum{ region{ momentum_matrix_elements{ direction = [ ..., ..., ... ] } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • type: vector of 3 real numbers: \((r_1, r_2, r_3)\)

  • values: no constraints

  • default: \(r_1=1.0\), \(r_2=0.0\), \(r_3=0.0\)

  • unit: \(\mathrm{-}\)

Functionality

It defines the polarization direction \(\epsilon\). From it a vector of unit length is calculated, which enters the calculation. In 1D simulation it can be omitted and [1,0,0] is then assumed.

output_matrix_elements

Calling sequence

quantum{ region{ momentum_matrix_elements{ output_matrix_elements = ... } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • type: choice

  • values: yes or no

  • default: yes

Functionality

If output_matrix_elements = yes then matrix elements are saved in output file.

output_transition_energies

Calling sequence

quantum{ region{ momentum_matrix_elements{ output_transition_energies = ... } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • type: choice

  • values: yes or no

  • default: no

Functionality

If output_transition_energies = yes then transition energies are saved in output file.

output_oscillator_strengths

Calling sequence

quantum{ region{ momentum_matrix_elements{ output_oscillator_strengths = ... } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • type: choice

  • values: yes or no

  • default: no

Functionality

If output_oscillator_strengths = yes then oscillator strengths are saved in output file. Currently, only a simple formula is used, i.e. the free electron mass is used and not the real effective mass one.

Gamma{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ Gamma{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle \Gamma_i | \epsilon\cdot\hat{\mathbf{p}} | \Gamma_j \rangle\).

X{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ X{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle X_i | \epsilon\cdot\hat{\mathbf{p}} | X_j \rangle\).

Delta{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ Delta{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle \Delta_i | \epsilon\cdot\hat{\mathbf{p}} | \Delta_j \rangle\).

L{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ L{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle L_i | \epsilon\cdot\hat{\mathbf{p}} | L_j \rangle\).

HH{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ HH{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle HH_i | \epsilon\cdot\hat{\mathbf{p}} | HH_j \rangle\).

LH{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ LH{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle LH_i | \epsilon\cdot\hat{\mathbf{p}} | LH_j \rangle\).

SO{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ SO{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\langle SO_i | \epsilon\cdot\hat{\mathbf{p}} | SO_j \rangle\).

KP6{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ KP6{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\sum_k \langle kp6_{k,i} | \epsilon\cdot\hat{\mathbf{p}} | kp6_{k,j} \rangle\), \(k\) = 1,…,6.

KP8{ }

Calling sequence

quantum{ region{ momentum_matrix_elements{ KP8{ } } } }

Properties

  • usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)

  • items: maximum 1

Functionality

Calculates the matrix element \(\sum_k \langle kp8_{k,i} | \epsilon\cdot\hat{\mathbf{p}} | kp8_{k,j} \rangle\), \(k\) = 1,…,8.

Last update: 27/05/2025