StateElectron

class sisl.physics.electron.StateElectron(state, parent=None, **info)

A state describing a physical quantity related to electrons

Attributes

dkind	The data-type of the state (in str)
dtype	Data-type for the state
info
parent
shape	Returns the shape of the state
state

Methods

Sk([format, spin])	Retrieve the overlap matrix corresponding to the originating parent structure.
__init__(state[, parent])	Define a state container with a given set of states
change_gauge(gauge)	In-place change of the gauge of the state coefficients
copy()	Return a copy (only the state is copied).
expectation(A[, diag])	Calculate the expectation value of matrix A
iter([asarray])	An iterator looping over the states in this system
norm()	Return a vector with the norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)
norm2([sum])	Return a vector with the norm of each state \(\langle\psi|\psi\rangle\)
normalize()	Return a normalized state where each state has \(|\psi|^2=1\)
outer([idx])	Return the outer product for the indices idx (or all if None) by \(\sum_i|\psi_i\rangle\langle\psi_i|\)
psi(grid[, spinor, eta])	Expand the coefficients as the wavefunction on grid as-is
spin_moment()	Calculate spin moment from the states
sub(idx)	Return a new state with only the specified states
wavefunction(grid[, spinor, eta])	Expand the coefficients as the wavefunction on grid as-is

Sk(format='csr', spin=None)

Retrieve the overlap matrix corresponding to the originating parent structure.

When self.parent is a Hamiltonian this will return \(\mathbf S(k)\) for the \(k\)-point these eigenstates originate from

Parameters:

format: str, optional

the returned format of the overlap matrix. This only takes effect for non-orthogonal parents.

spin : Spin, optional

for non-collinear spin configurations the fake overlap matrix returned will have halve the size of the input matrix. If you want the full overlap matrix, simply do not specify the spin argument.

change_gauge(gauge)

In-place change of the gauge of the state coefficients

The two gauges are related through:

\[\tilde C_j = e^{i\mathbf k\mathbf r_j} C_j\]

where \(C_j\) belongs to the gauge R and \(\tilde C_j\) is in the gauge r.

Parameters:

gauge : {‘R’, ‘r’}

specify the new gauge for the state coefficients

copy()

Return a copy (only the state is copied). parent and info are passed by reference

dkind

The data-type of the state (in str)

dtype

Data-type for the state

expectation(A, diag=True)

Calculate the expectation value of matrix A

The expectation matrix is calculated as:

\[A_{ij} = \langle \psi_i | \mathbf A | \psi_j \rangle\]

If diag is true, only the diagonal elements are returned.

Parameters:

A : array_like

a vector or matrix that expresses the operator A

diag : bool, optional

whether only the diagonal elements are calculated or if the full expectation matrix is calculated

Returns:

expectation : a vector if diag is true, otherwise the expectation matrix

info

iter(asarray=False)

An iterator looping over the states in this system

Parameters:

asarray: bool, optional

if true the yielded values are the state vectors, i.e. a numpy array. Otherwise an equivalent object is yielded.

Yields:

state : State

a state only containing individual elements, if asarray is false

state : numpy.ndarray

a state only containing individual elements, if asarray is true

norm()

Return a vector with the norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)

Returns:

numpy.ndarray

the normalization for each state

norm2(sum=True)

Return a vector with the norm of each state \(\langle\psi|\psi\rangle\)

Parameters:

sum : bool, optional

if true the summed orbital square is returned (a vector). For false a matrix with normalization squared per orbital is returned.

Returns:

numpy.ndarray

the normalization on each orbital for each state

normalize()

Return a normalized state where each state has \(|\psi|^2=1\)

This is roughly equivalent to:

>>> state = State(np.arange(10))
>>> n = state.norm()
>>> norm_state = State(state.state / n.reshape(-1, 1))

Returns:

State

a new state with all states normalized, otherwise equal to this

outer(idx=None)

Return the outer product for the indices idx (or all if None) by \(\sum_i|\psi_i\rangle\langle\psi_i|\)

Parameters:

idx : int or array_like, optional

only perform an outer product of the specified indices, otherwise all states are used

Returns:

numpy.ndarray

a matrix with the sum of outer state products

parent

psi(grid, spinor=0, eta=False)

Expand the coefficients as the wavefunction on grid as-is

See wavefunction for argument details.

shape

Returns the shape of the state

spin_moment()

Calculate spin moment from the states

This routine calls spin_moment with appropriate arguments and returns the spin moment for the states.

See spin_moment for details.

state

sub(idx)

Return a new state with only the specified states

Parameters:

idx : int or array_like

indices that are retained in the returned object

Returns:

State

a new state only containing the requested elements

wavefunction(grid, spinor=0, eta=False)

Expand the coefficients as the wavefunction on grid as-is

See wavefunction for argument details.