wavepacket.operator

This module contains classes that define operators on a given grid.

Classes

`OperatorBase`	Base class of an operator.
`CartesianKineticEnergy`	Convenience class that implements the common Cartesian kinetic energy operator.
`PlaneWaveFbrOperator`	Base class for operators that are diagonal in a plane wave basis.
`Potential1D`	Operator that represents a real-valued one-dimensional potential.

Functions

expectation_value(→ complex)

Calculates the expectation value of an operator for a given state.

Package Contents

class wavepacket.operator.OperatorBase(grid: wavepacket.grid.Grid)

Bases: abc.ABC

Base class of an operator.

An operator can be applied to a wave function or from the left or right to a density operator. It is defined on a grid, and can only operate on states on that grid.

Parameters:

gridwp.grid.Grid: The grid on which the operator is defined. Particular operators may require additional parameters.

Attributes:

grid

property grid: Returns the grid on which the operator is defined.

apply(state: wavepacket.grid.State, t: float | None = None) → wavepacket.grid.State

Applies the operator onto a wave function or a density operator from the left.

This is a convenience function if you just want to apply the operator without detailed knowledge of the state.

Parameters:

statewp.grid.State

The state that the operator is applied on.

tfloat, optional

The time at which the operator is applied.: The default value None raises an exception for time-dependent operators.

Returns:

wp.grid.State: The result of applying the operator on the state.

Raises:

wp.BadGridError: If the state’s grid does not match the grid of the operator.
wp.BadStateError: If the state is neither a wave function nor a density operator.

abstractmethod apply_to_wave_function(psi: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a wave function.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

psiwpt.ComplexData: The coefficients describing the wave function on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting wave function.

abstractmethod apply_from_left(rho: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a density operator from the left.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

rhowpt.ComplexData: The coefficients describing the density operator on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting density operator.

abstractmethod apply_from_right(rho: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a density operator from the right.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

rhowpt.ComplexData: The coefficients describing the density operator on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting density operator.

wavepacket.operator.expectation_value(op: wavepacket.operator.operatorbase.OperatorBase, state: wavepacket.grid.State, t: float | None = None) → complex

Calculates the expectation value of an operator for a given state.

Parameters:

opwp.operator.OperatorBase

The operator whose expectation value is calculated.

statewp.grid.State

The wave function or density operator that is used for the calculation.

tfloat, optional

The time at which the operator should be evaluated.: Only required for time-dependent operators, where the default value None raises an exception.

class wavepacket.operator.CartesianKineticEnergy(grid: wavepacket.grid.Grid, dof_index: int, mass: float)

Bases: PlaneWaveFbrOperator

Convenience class that implements the common Cartesian kinetic energy operator.

The form of the operator is $-\frac{1}{2m} \ \frac{\partial^2}{\partial x^2}$ . It requires the degree of freedom to be a wavepacket.grid.PlaneWaveDof.

Parameters:

gridwp.grid.Grid: The grid on which the operator is defined.
dof_indexinst: Degree of freedom along which the operator acts
massfloat: The mass of the particle.

Raises:

wp.InvalidValueError: If the mass is not positive, or if the degree of freedom does not describe a plane wave expansion.

class wavepacket.operator.PlaneWaveFbrOperator(grid: wavepacket.grid.Grid, dof_index: int, generator: wavepacket.typing.Generator)

Bases: wavepacket.operator.operatorbase.OperatorBase

Base class for operators that are diagonal in a plane wave basis.

The wavepacket.grid.PlaneWaveDof describes an expansion of the wave function in plane waves. In the corresponding FBR, derivatives are diagonal and essentially transform into a multiplication with the wave vector / FBR grid.

A key difference to a generic FBR operator is that this operator does not apply the shift after the FFT, which increases performance.

Parameters:

gridwp.grid.Grid: The grid on which the operator is defined.
dof_indexint: The degree of freedom along which the operator is defined.
generatorwpt.Generator: A callable that gives the operator value for each FBR point.

Raises:

wp.InvalidValueError: If the supplied degree of freedom is not a plane wave expansion.

apply_to_wave_function(psi: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a wave function.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

psiwpt.ComplexData: The coefficients describing the wave function on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting wave function.

apply_from_left(rho: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a density operator from the left.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

rhowpt.ComplexData: The coefficients describing the density operator on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting density operator.

apply_from_right(rho: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a density operator from the right.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

rhowpt.ComplexData: The coefficients describing the density operator on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting density operator.

class wavepacket.operator.Potential1D(grid: wavepacket.grid.Grid, dof_index: int, generator: wavepacket.typing.RealGenerator)

Bases: wavepacket.operator.operatorbase.OperatorBase

Operator that represents a real-valued one-dimensional potential.

Within the DVR approximation [1], potential energy operators are diagonal in the DVR. That is, they are completely described by a value for each grid point.

Parameters:

gridwp.grid.Grid: The grid on which the operator is defined
dof_indexint: the index of the degree of freedom along which the potential is defined.
generatorwpt.RealGenerator: A callable that generates a potential energy value for each grid point of the respective DOF.

References

[1]

https://sourceforge.net/p/wavepacket/wiki/Numerics.DVR>

apply_to_wave_function(psi: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a wave function.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

psiwpt.ComplexData: The coefficients describing the wave function on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting wave function.

apply_from_left(rho: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a density operator from the left.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

rhowpt.ComplexData: The coefficients describing the density operator on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting density operator.

apply_from_right(rho: wavepacket.typing.ComplexData, t: float) → wavepacket.typing.ComplexData

Applies the operator on a density operator from the right.

This function is mainly for Wavepacket-internal use. It ignores most error handling (usually done by the wrapping wavepacket.expression.ExpressionBase), and operates directly on coefficients to avoid the creation of temporary states.

Parameters:

rhowpt.ComplexData: The coefficients describing the density operator on which the operator acts.
tfloat: The time at which the operator should be evaluated.

Returns:

wpt.ComplexData: The coefficients of the resulting density operator.