Name

calculateProjectedHamiltonianEigenstates Calculates the eigenstates of atoms in the central region.

Synopsis

Namespace: ATK.TwoProbe
list calculateProjectedHamiltonianEigenstates(
self_consistent_calculation,
projection_atoms,
quantum_numbers
)

Description

Calculates the molecular wave functions corresponding to the eigenstates of the molecular projected self-consistent Hamiltonian (MPSH). The MPSH is defined as the Hamiltonian of a two-probe system projected onto a subset of atoms in the scattering region.

List of arguments

self_consistent_calculation

An object returned from a previously performed self-consistent calculation for a TwoProbeConfiguration.

Default: None

projection_atoms

A list of atom indices in the scattering region onto which to project the two-probe Hamiltonian. The indices are integers in the range from 0 to N-1, where N is the number of atoms in the scattering region, as defined during the setup of the TwoProbeConfiguration.

Default: None

quantum_numbers

The quantum numbers which determine the eigenstates to be calculated (see below).

Default: None

Returned object methods

Each object in the list corresponds to an Eigenstate object, and has the following query methods:

  • Array toArray(): Returns the real-space representation of the cell-function (i.e. the periodic part of the eigenstate) as complex numbers in a NumPy array with dimensions (n1, n2, n3).

  • PhysicalUnit toUnit(): Returns the unit of the real-space representation of the eigenstate.

  • Tuple quantumNumber(): Returns the quantum numbers of the eigenstate. The format of the quantum depends on the type of system (see below).

  • PhysicalQuantity eigenvalue(): Returns the eigenvalue of the eigenstate.

Usage examples

Calculate the projected eigenstates for the two lowest energy levels with spin up:

eigenstates=calculateProjectedHamiltonianEigenstates(
    self_consistent_calculation=self_consistent_calculation,
    projection_atoms = (3,4),
    quantum_numbers = ((0,1),Spin.Up)
    )

Notes

The quantum numbers are defined in the following way:

  • n - for spin-unpolarized systems

  • (n,spin) - for spin-unpolarized systems

where n is a non-negative integer (or a sequence of integers) representing the quantum number of an energy level and the spin state Spin.Up/Spin.Down. The ordering of the returned eigenstates in the returned list is such that the first element in the quantum number sequence varies slowest and the last element fastest.