ObservablesMixedHAWP¶

About the `ObservablesMixedHAWP` class¶

The WaveBlocks Project

Inheritance diagram¶

Class documentation¶

class WaveBlocksND.ObservablesMixedHAWP(*, innerproduct=None, gradient=None)[source]¶

This class implements the mixed case observable computation $\langle \Psi | \cdot | \Psi^{\prime} \rangle$ for Hagedorn wavepackets $\Psi$ where the bra $\Psi$ does not equal the ket $\Psi^{\prime}$ .

kinetic_energy(wavepacket, *, component=None, summed=False)[source]¶

Compute the kinetic energy $E_{\text{kin}} := \langle \Psi | T | \Psi \rangle$ of the different components $\Phi_i$ of the wavepacket $\Psi$ .

Parameters:

wavepacket (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi$ of which we compute the kinetic energy.
component (Integer or None.) – The index $i$ of the component $\Phi_i$ whose kinetic energy we compute. If set to None the computation is performed for all $N$ components.
summed (Boolean, default is False.) – Whether to sum up the kinetic energies $E_i$ of the individual components $\Phi_i$ .

Returns:

A list of the kinetic energies of the individual components or the overall kinetic energy of the wavepacket. (Depending on the optional arguments.)

Note

This method just expands to a call of the ObservablesMixedHAWP.kinetic_overlap_energy() method. Better use ObservablesHAWP.kinetic_energy().

kinetic_overlap_energy(pacbra, packet, *, component=None, summed=False)[source]¶

Compute the kinetic energy overlap $\langle \Psi | T | \Psi^{\prime} \rangle$ of the different components $\Phi_i$ and $\Phi_i^{\prime}$ of the wavepackets $\Psi$ and $\Psi^{\prime}$ .

Parameters:

pacbra (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi$ which takes part in the kinetic energy integral.
packet (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi^{\prime}$ which takes part in the kinetic energy integral.
component (Integer or None.) – The index $i$ of the components $\Phi_i$ of $\Psi$ and $\Phi_i^{\prime}$ of $\Psi^{\prime}$ which take part in the kinetic energy integral. If set to None the computation is performed for all $N$ components of $\Psi$ and $\Psi^{\prime}$ .
summed (Boolean, default is False.) – Whether to sum up the kinetic energies $E_i$ of the individual components $\Phi_i$ and $\Phi_i^{\prime}$ .

Returns:

A list of the kinetic energy overlap integrals of the individual components or the overall kinetic energy overlap of the wavepackets. (Depending on the optional arguments.)

norm(wavepacket, *, component=None, summed=False)[source]¶

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

Parameters:

wavepacket (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi$ of which we compute the norm.
component (int or None.) – The index $i$ of the component $\Phi_i$ whose norm is computed. The default value is None which means to compute the norms of all $N$ components.
summed (Boolean, default is False.) – Whether to sum up the norms $\langle \Phi_i | \Phi_i \rangle$ of the individual components $\Phi_i$ .

Returns:

The norm of $\Psi$ or the norm of $\Phi_i$ or a list with the $N$ norms of all components. (Depending on the optional arguments.)

Note

This method just redirects to a call to HagedornWavepacketBase.norm().

overlap(pacbra, packet, *, component=None, summed=False)[source]¶

Calculate the overlap $\langle \Psi | \Psi^{\prime} \rangle$ of the wavepackets $\Psi$ and $\Psi^{\prime}$ .

Parameters:

pacbra (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi$ which takes part in the overlap integral.
packet (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi^{\prime}$ which takes part in the overlap integral.
component (Integer or None.) – The index $i$ of the components $\Phi_i$ of $\Psi$ and $\Phi_i^{\prime}$ of $\Psi^{\prime}$ whose overlap is computed. The default value is None which means to compute the overlaps with all $N$ components involved.
summed (Boolean, default is False.) – Whether to sum up the overlaps $\langle \Phi_i | \Phi_i^{\prime} \rangle$ of the individual components $\Phi_i$ and $\Phi_i^{\prime}$ .

Returns:

The overlap of $\Psi$ with $\Psi^{\prime}$ or the overlap of $\Phi_i$ with $\Phi_i^{\prime}$ or a list with the $N$ overlaps of all components. (Depending on the optional arguments.)

potential_energy(wavepacket, potential, *, component=None, summed=False)[source]¶

Compute the potential energy $E_{\text{pot}} := \langle \Psi | V(x) | \Psi \rangle$ of the different components $\Phi_i$ of the wavepacket $\Psi$ .

Parameters:

wavepacket (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi$ of which we compute the potential energy.
potential – The potential $V(x)$ . (Actually, not the potential object itself but one of its V.evaluate_* methods.)
component (Integer or None.) – The index $i$ of the component $\Phi_i$ whose potential energy we compute. If set to None the computation is performed for all $N$ components.
summed (Boolean, default is False.) – Whether to sum up the potential energies $E_i$ of the individual components $\Phi_i$ .

Returns:

A list of the potential energies of the individual components or the overall potential energy of the wavepacket. (Depending on the optional arguments.)

Note

This method just expands to a call of the ObservablesMixedHAWP.potential_overlap_energy() method. Better use ObservablesHAWP.potential_energy().

potential_overlap_energy(pacbra, packet, potential, *, component=None, summed=False)[source]¶

Compute the potential energy overlap $\langle \Psi | V(x) | \Psi^{\prime} \rangle$ of the different components $\Phi_i$ and $\Phi_i^{\prime}$ of the wavepackets $\Psi$ and $\Psi^{\prime}$ .

Parameters:

pacbra (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi$ which takes part in the potential energy integral.
packet (A HagedornWavepacketBase subclass instance.) – The wavepacket $\Psi^{\prime}$ which takes part in the potential energy integral.
potential – The potential $V(x)$ . (Actually, not the potential object itself but one of its V.evaluate_* methods.)
component (Integer or None.) – The index $i$ of the components $\Phi_i$ of $\Psi$ and $\Phi_i^{\prime}$ of $\Psi^{\prime}$ which take part in the potential energy integral. If set to None the computation is performed for all $N$ components of $\Psi$ and $\Psi^{\prime}$ .
summed (Boolean, default is False.) – Whether to sum up the potential energies $E_i$ of the individual components $\Phi_i$ and $\Phi_i^{\prime}$ .

Returns:

A list of the potential energy overlap integrals of the individual components or the overall potential energy overlap of the wavepackets. (Depending on the optional arguments.)

set_gradient(gradient)[source]¶

Set the gradient.

Parameters:	gradient (A `Gradient` subclass instance.) – A gradient operator. The gradient is only used for the computation of the kinetic energy $\langle \Psi \| T \| \Psi^{\prime} \rangle$ .

set_innerproduct(innerproduct)[source]¶

Set the innerproduct.

Parameters:	innerproduct (A `InnerProduct` subclass instance.) – An inner product for computing the integrals. The inner product is used for the computation of all brakets $\langle \Psi \| \cdot \| \Psi^{\prime} \rangle$ .

Note

Make sure to use an inhomogeneous inner product here.

ObservablesMixedHAWP¶

About the `ObservablesMixedHAWP` class¶

Inheritance diagram¶

Class documentation¶

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ObservablesMixedHAWP¶

About the ObservablesMixedHAWP class¶

Inheritance diagram¶

Class documentation¶

About the `ObservablesMixedHAWP` class¶