HagedornWavepacketInhomogeneous¶

About the `HagedornWavepacketInhomogeneous` class¶

The WaveBlocks Project

Inheritance diagram¶

Inheritance diagram of HagedornWavepacketInhomogeneous

Class documentation¶

class WaveBlocks.HagedornWavepacketInhomogeneous(parameters)¶

This class represents inhomogeneous vector valued wavepackets $|\Psi\rangle$ .

coefficients = None¶: The coefficients $c^i$ of the linear combination for each component $\Phi_i$ .

evaluate_at(nodes, component=None, prefactor=False)¶

Evaluete the Hagedorn wavepacket $\Psi$ at the given nodes $\gamma$ .

Parameters:	nodes – The nodes $\gamma$ at which the Hagedorn wavepacket gets evaluated. component – The index $i$ of a single component $\Phi_i$ to evaluate. (Defaults to ‘None’ for evaluating all components.) prefactor – Whether to include a factor of $\left(\det\left(Q_i\right)\right)^{-\frac{1}{2}}$ .
Returns:	A list of arrays or a single array containing the values of the $\Phi_i$ at the nodes $\gamma$ .

evaluate_basis_at(nodes, component, prefactor=False)¶

Evaluate the Hagedorn functions $\phi_k$ recursively at the given nodes $\gamma$ .

Parameters:	nodes – The nodes $\gamma$ at which the Hagedorn functions are evaluated. component – The index $i$ of the component whose basis functions $\phi^i_k$ we want to evaluate. prefactor – Whether to include a factor of $\left(\det\left(Q_i\right)\right)^{-\frac{1}{2}}$ .
Returns:	Returns a twodimensional array $H$ where the entry $H[k,i]$ is the value of the $k$ -th Hagedorn function evaluated at the node $i$ .

gen_id()¶: Generate an (unique) ID per wavepacket instance.

get_basis_size(component=None)¶

Returns:	The size of the basis, i.e. the number $K$ of ${\phi_k}_{k=1}^K$ .

get_coefficient_vector()¶

Returns:	The coefficients $c^i$ of all components $\Phi_i$ as a single long column vector.

get_coefficients(component=None)¶

Returns the coefficients $c^i$ for some components $\Phi_i$ of $|\Psi\rangle$ .

Parameters:	component – The index $i$ of the coefficients $c^i$ we want to get.
Returns:	The coefficients $c^i$ either for all components $\Phi_i$ or for a specified one.

get_id()¶: Return the packet ID of this wavepacket instance. The ID may be used for storing packets in associative lists.

get_norm(component=None, summed=False)¶

Calculate the $L^2$ norm of the wavepacket $|\Psi\rangle$ .

Parameters:	component – The component $\Phi_i$ of which the norm is calculated. summed – Whether to sum up the norms of the individual components $\Phi_i$ .
Returns:	A list containing the norms of all components $\Phi_i$ or the overall norm of $\Psi$ .

get_number_components()¶

Returns:	The number $N$ of components the wavepacket $\Psi$ has.

get_parameters(component=None, aslist=False)¶

Get the Hagedorn parameters $\Pi_i$ of each component $\Phi_i$ of the wavepacket $\Psi$ .

Parameters:	component – The index $i$ of the component whose parameters $\Pi_i$ we want to get. aslist – Dummy parameter for API compatibility with the homogeneous packets.
Returns:	A list with all the sets $\Pi_i$ or a single set.

get_quadrature()¶

Return the InhomogeneousQuadrature instance used for evaluating brakets.

Returns:	The current instance `InhomogeneousQuadrature`.

grady(component)¶

Calculate the effect of $-i \epsilon^2 \frac{\partial}{\partial x}$ on a component $\Phi_i$ of the Hagedorn wavepacket $\Psi$ .

Parameters:	component – The index $i$ of the component $\Phi_i$ on which we apply the above operator.
Returns:	The modified coefficients.

kinetic_energy(summed=False)¶

Calculate the kinetic energy $\langle\Psi|T|\Psi\rangle$ of the wavepacket componentwise.

Parameters:	summed – Wheter to sum up the individual integrals $\langle\Phi_i\|T_{i,j}\|\Phi_j\rangle$ .
Returns:	The kinetic energy of the wavepacket’s components $\Phi_i$ or the overall kinetic energy of $\Psi$ .

number_components = None¶: Number of components $\Phi_i$ the wavepacket $|\Psi\rangle$ has got.

parameters = None¶: Data structure that contains the Hagedorn parameter sets $\Pi_i$ of each component $\Phi_i$ . The parameter values are initialized to the Harmonic Oscillator Eigenfunctions

potential_energy(potential, summed=False)¶

Calculate the potential energy $\langle\Psi|V|\Psi\rangle$ of the wavepacket componentwise.

Parameters:	potential – The potential energy operator $V$ as function. summed – Wheter to sum up the individual integrals $\langle\Phi_i\|V_{i,j}\|\Phi_j\rangle$ .
Returns:	The potential energy of the wavepacket’s components $\Phi_i$ or the overall potential energy of $\Psi$ .

project_to_canonical(potential)¶

Project the Hagedorn wavepacket into the canonical basis.

Parameters:	potential – The potential $V$ whose eigenvectors $nu_l$ are used for the transformation.

Note

This function is expensive and destructive! It modifies the coefficients of the self instance.

project_to_eigen(potential)¶

Project the Hagedorn wavepacket into the eigenbasis of a given potential $V$ .

Parameters:	potential – The potential $V$ whose eigenvectors $nu_l$ are used for the transformation.

Note

This function is expensive and destructive! It modifies the coefficients of the self instance.

quadrature = None¶: An object that can compute brakets via quadrature.

set_basis_size(basis_size, component=None)¶

Set the size of the basis of a given component or all components.

Parameters:	basis_size – An single positive integer or a list of $N$ positive integers. component – The component for which we want to set the basis size. Default is `None` which means ‘all’.

set_coefficient(component, index, value)¶

Set a single coefficient $c^i_k$ of the specified component $\Phi_i$ of $|\Psi\rangle$ .

Raises ValueError:
Parameters:	component – The index $i$ of the component $\Phi_i$ we want to update. index – The index $k$ of the coefficient $c^i_k$ we want to update. value – The new value of the coefficient $c^i_k$ .
	For invalid indices $i$ or $k$ .

set_coefficient_vector(vector)¶

Set the coefficients for all components $\Phi_i$ simultaneously.

Parameters:	vector – The coefficients of all components as a single long column vector.

Note

This function does NOT copy the input data! This is for efficiency as this routine is used in the innermost loops.

set_coefficients(values, component=None)¶

Update the coefficients $c$ of $\Psi$ .

Raises ValueError:
Parameters:	values – The new values of the coefficients $c^i$ of $\Phi_i$ . component – The index $i$ of the component we want to update with new coefficients.
	For invalid indices $i$ .

Note

This function can either set new coefficients for a single component $\Phi_i$ only if the component attribute is set or for all components simultaneously if values is a list of arrays.

set_id(anid)¶: Manually set an ID for the current wavepacket instance.

set_parameters(parameters, component=None)¶

Set the Hagedorn parameters $\Pi_i$ of each component $\Phi_i$ of the wavepacket $\Psi$ .

Parameters:	parameters – A list or a single set of Hagedorn parameters. component – The index $i$ of the component whose parameters $\Pi_i$ we want to update.

set_quadrature(quadrature)¶

Set the InhomogeneousQuadrature instance used for evaluating brakets.

Parameters:	quadrature – The new `InhomogeneousQuadrature` instance. May be `None` to use a dafault one with a quadrature rule of order $K+4$ .

to_fourier_space(assign=True)¶

Transform the wavepacket to Fourier space.

Parameters:	assign – Whether to assign the transformation to this packet or return a cloned packet.

Note

This is the inverse of the method to_real_space().

to_real_space(assign=True)¶

Transform the wavepacket to real space.

Parameters:	assign – Whether to assign the transformation to this packet or return a cloned packet.

Note

This is the inverse of the method to_fourier_space().

HagedornWavepacketInhomogeneous¶

About the `HagedornWavepacketInhomogeneous` class¶

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Class documentation¶

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HagedornWavepacketInhomogeneous¶

About the HagedornWavepacketInhomogeneous class¶

Inheritance diagram¶

Class documentation¶

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About the `HagedornWavepacketInhomogeneous` class¶