# Difference between revisions of "Tutorial:Kronig-Penney Model"

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{{variable|Dimensions|System}} = 1 | {{variable|Dimensions|System}} = 1 | ||

{{variable|TheoryLevel|Hamiltonian}} = independent_particles | {{variable|TheoryLevel|Hamiltonian}} = independent_particles | ||

− | + | ||

a = 5 | a = 5 | ||

b = 1 | b = 1 |

## Revision as of 19:03, 14 March 2019

In this tutorial we calculate the bandstructure for Kronig-Penney Model. The Kronig-Penney Model is a simplified 1D electron in a lattice, where the lattice is a series of potential barriers.

## Input

The following input file will be used for the ground state calculation:

`CalculationMode`

= gs`ExtraStates`

= 4`PeriodicDimensions`

= 1`Dimensions`

= 1`TheoryLevel`

= independent_particles a = 5 b = 1 V = 3

`Lsize`

= (a + b)/2

`Spacing`

= .005

`%``Species`

"B" | species_user_defined | potential_formula | "(x>-b)*V*(x<0)" | valence | 1
%

`%``Coordinates`

"B" | 0 |
%

`%``KPointsGrid`

11 |
%

`%``KPointsPath`

11 |
0.0 |
0.5 |
%

`ConvEigenError`

= true

## Bandstructure

To calculate the bandstructure simply change the input file to the following:

`CalculationMode`

= unocc`ExtraStates`

= 4`PeriodicDimensions`

= 1`Dimensions`

= 1`TheoryLevel`

= independent_particles

a = 5 b = 1 V = 3

`Lsize`

= (a + b)/2

`Spacing`

= .005

`%``Species`

"B" | species_user_defined | potential_formula | "(x>-b)*V*(x<0)" | valence | 1
%

`%``Coordinates`

"B" | 0 |
%

`%``KPointsGrid`

11 |
%

`%``KPointsPath`

11 |
0.0 |
0.5 |
%

`ConvEigenError`

= true