Hamiltonian¶

class siegpy.hamiltonian.Hamiltonian(potential, coord_map, filters=<siegpy.filters.WaveletFilters object>)[source]¶

Bases: object

A Hamiltonian has to be defined when one is interested in finding numerically the Siegert states of a potential when the eigenstates are not known analytically.

A Hamiltonian is defined by a potential and a coordinate mapping, which gives rise to extra potentials to be added, known as the Reflection-Free Complex Absorbing Potentials (RF-CAP).

Filters allowing to define the gradient and laplacian operators are also required. The default value corresponds to Daubechies Wavelet filters.

Parameters:	potential (Potential) – Potential studied. coord_map (CoordMap) – Coordinate mapping used. filters (Filters) – Filters used to define the Hamiltonian matrix.

potential¶

Returns:	Potential considered.
Return type:	Potential

coord_map¶

Returns:	Complex scaling considered.
Return type:	CoordMap

filters¶

Returns:	Filters used to define the matrices.
Return type:	Filters

gradient_matrix¶

Returns:	Gradient matrix used to define the matrices.
Return type:	2D numpy array

laplacian_matrix¶

Returns:	Laplacian matrix used to define the matrices.
Return type:	2D numpy array

magic_matrix¶

Returns:	Magic filter matrix used to define the matrices.
Return type:	2D numpy array

matrix¶

Returns:	Hamiltonian matrix.
Return type:	2D numpy array

virial_matrix¶

Returns:	Virial operator matrix.
Return type:	2D numpy array

_find_hamiltonian_matrix()[source]¶

Evaluate the Hamiltonian matrix.

Returns:	Hamiltonian matrix.
Return type:	2D numpy array

_find_virial_matrix()[source]¶

Evaluate the virial operator matrix.

Returns:	Virial operator matrix.
Return type:	2D numpy array

_build_virial_matrix(U0, U1, U2, U11)[source]¶

Build the matrix operator given a set of virial potentials.

Parameters:	U0 (numpy array) – First virial potential. U1 (numpy array) – Second virial potential. U2 (numpy array) – Thirs virial potential. U11 (numpy array) – Fourth virial potential.
Returns:	Virial operator as a matrix.
Return type:	2D numpy array

solve(max_virial=None)[source]¶

Find the eigenstates of the potential and evaluate the virial for each of them. This is the main method of the Hamiltonian class.

Parameters:	max_virial – Maximal virial value for a state to be considered as a Siegert state.
Returns:	Basis set made of the eigenstates of the Hamiltonian.
Return type:	BasisSet

_pot_to_mat(potential_values)[source]¶

Convert the potential values to a diagonal matrix.

Parameters:	potential_values (numpy array) – Values of a potential.
Returns:	Potential as a diagonal matrix.
Return type:	2D numpy array