qml.qchem.spinz¶
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spinz
(orbitals)[source]¶ Computes the total spin projection observable \(\hat{S}_z\).
The total spin projection operator \(\hat{S}_z\) is given by
\[\hat{S}_z = \sum_{\alpha, \beta} \langle \alpha \vert \hat{s}_z \vert \beta \rangle ~ \hat{c}_\alpha^\dagger \hat{c}_\beta, ~~ \langle \alpha \vert \hat{s}_z \vert \beta \rangle = s_{z_\alpha} \delta_{\alpha,\beta},\]where \(s_{z_\alpha} = \pm 1/2\) is the spin-projection of the single-particle state \(\vert \alpha \rangle\). The operators \(\hat{c}^\dagger\) and \(\hat{c}\) are the particle creation and annihilation operators, respectively.
- Parameters
orbitals (str) – Number of spin orbitals. If an active space is defined, this is the number of active spin-orbitals.
- Returns
the total spin projection observable \(\hat{S}_z\)
- Return type
- Raises
ValueError – If orbitals is less than or equal to 0
Example
>>> orbitals = 4 >>> print(spinz(orbitals)) ( -0.25 * Z(0) + 0.25 * Z(1) + -0.25 * Z(2) + 0.25 * Z(3) )
code/api/pennylane.qchem.spinz
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