a1g

Module: luescher_nd.operators.a1g

Implements operators to project on A1g states

complement(n1d, ndim)[source]

Computes one minus get_projector_to_a1g

Parameters
  • n1d (int) – Number of points in one direction.

  • ndim (int) – Number of spatial dimensions.

Return type

csr_matrix

projector(n1d, ndim)[source]

Implements the projection operator \(\ket{A_{1g}}\bra{A_{1g}}\).

Because A1g is espeically simple, the procedure works in any dimension, specified by ndim.

If you have a wavefunction \( \ket{\psi} \) written as a sum of plane waves, applying this operator will give you

$$ \sum_{j \in A_{1g}} \ket{j}\braket{j | \psi} $$

If \( \ket{\psi} \) isn’t already in momentum space, who knows what this will do!

Parameters
  • n1d (int) – Number of points in one direction.

  • ndim (int) – Number of spatial dimensions.

Return type

csr_matrix

reducer(n1d, ndim)[source]

Implements the projection operator that’s \(\ket{A_{1g}}\bra{A_{1g}}\). Because A1g is espeically simple, the procedure works in any dimension, specified by ndim.

If you have a wavefunction \( \ket{\psi} \) written as a sum of plane waves, applying this operator will give you

$$ \sum_{j \in A_{1g}} \ket{j}\braket{j | \psi} $$

If \( \ket{\psi} \) isn’t already in momentum space, who knows what this will do!

Parameters
  • n1d (int) – Number of points in one direction.

  • ndim (int) – Number of spatial dimensions.

Return type

ndarray