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