GradientHAWPpsi¶

About the `GradientHAWPpsi` class¶

The WaveBlocks Project

Inheritance diagram¶

Class documentation¶

class WaveBlocksND.GradientHAWPpsi[source]¶

This class implements the computation of the action of the gradient operator $-i \varepsilon^2 \nabla_x$ applied to a new-kind Hagedorn wavepacket $\Psi$ .

apply_gradient(wavepacket, *, component=None, as_packet=True)¶

Compute the effect of the gradient operator $-i \varepsilon^2 \nabla_x$ on the basis functions $\phi(x)$ of a component $\Phi_i$ of the Hagedorn wavepacket $\Psi$ .

Parameters:	wavepacket (A `HagedornWavepacketBase` subclass instance.) – The wavepacket $\Psi$ containing $\Phi_i$ . component (Integer or `None`.) – The index $i$ of the component $\Phi_i$ . as_packet (Boolean, default is `True`.) – Whether to return a full packet.
Returns:	A list of length $N$ or a single pair of extended basis shapes $\mathfrak{\dot{K}}_i$ and new coefficients $c^\prime_i$ . If requested, copies of the original wavepacket are returned with these new values set. There are $D$ packets, one for each space variable component $\partial_{x_d}$ of the gradient.

apply_gradient_component(wavepacket, component)[source]¶

Compute the effect of the gradient operator $-i \varepsilon^2 \nabla_x$ on the basis functions $\psi(x)$ of a component $\Phi_i$ of the new-kind Hagedorn wavepacket $\Psi$ .

Parameters:	wavepacket (A `HagedornWavepacketBase` subclass instance.) – The wavepacket $\Psi$ containing $\Phi_i$ . component (Integer.) – The index $i$ of the component $\Phi_i$ .
Returns:	Extended basis shape $\mathfrak{\dot{K}}$ and new coefficients $c^\prime$ for component $\Phi_i$ . The coefficients are stored column-wise with one column per dimension $d$ . The $c^\prime$ array is of shape $\|\mathfrak{\dot{K}}\| \times D$ .