EigenvectorElectron¶
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class
sisl.physics.
EigenvectorElectron
(state, parent=None, **info)[source]¶ Eigenvectors of electronic states, no eigenvalues retained
This holds routines that enable the calculation of spin moments.
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 fromParameters: - 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.
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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 gauger
.Parameters: - gauge : {‘R’, ‘r’}
specify the new gauge for the state coefficients
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copy
()¶ Return a copy (only the state is copied).
parent
andinfo
are passed by reference
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dkind
¶ The data-type of the state (in str)
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dtype
¶ Data-type for the state
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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
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info
¶
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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
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norm
()¶ Return a vector with the norm of each state \(\sqrt{\langle\psi|\psi\rangle}\)
Returns: - numpy.ndarray
the normalization for each state
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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
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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
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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
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parent
¶
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psi
(grid, spinor=0, eta=False)¶ Expand the coefficients as the wavefunction on grid as-is
See
wavefunction
for argument details.
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shape
¶ Returns the shape of the state
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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.
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state
¶
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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
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wavefunction
(grid, spinor=0, eta=False)¶ Expand the coefficients as the wavefunction on grid as-is
See
wavefunction
for argument details.
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