AnalyticEigenstates

The classes documented below are the base classes you should consider subclassing before adding a new analytical case to the SiegPy module.

The AnalyticEigenstate class is the base class for two other classes:

• the AnalyticSiegert class,
• and the AnalyticContinuum class.

If your analytic case is already well defined by these last classes, you may only subclass these two. However, if you need to add some methods or attributes to both classes, you may also subclass AnalyticEigenstate.

For instance, the parity of the analytic eigenstates in the 1D Square-Well Potential case made it mandatory.

class siegpy.analyticeigenstates.AnalyticEigenstate(k, potential, grid, analytic)

Bases: siegpy.functions.AnalyticFunction, siegpy.eigenstates.Eigenstate

Class gathering the attributes and methods necessary to define an analytic eigenstate of any analytical problem (such as the 1D Square-Well Potential case).

Note

To consider a case as analytic, the wavefunctions of the Siegert and continuum states should be known analytically. The analytic scalar product of both types of eigenstates with at least one type of test function should also be defined.

Parameters:

• k (complex) – Wavenumber of the eigenstate.
• potential (Potential) – Potential for which the analytic eigenstate is known.
• grid (list or set or numpy array) – Discretization grid.
• analytic (bool) – If True, the scalar products must be computed analytically.

Raises:

WavenumberError – If the inferred Siegert type is unknown.

potential

Returns:Potential for which the eigenstate is a solution. Return type:complex or float

wavenumber

Returns:Wavenumber of the eigenstate. Return type:complex or float

energy

Returns:Energy of the Eigenstate Return type:complex or float

_find_Siegert_type(k)

Note

This is an asbtract method.

Parameters:k (float or complex) – Wavenumber of the eigenstate Returns:Type of the eigenstate from its wavenumber k ('b' for bound states, 'ab' for anti-bound states, 'r' for resonant states, 'ar' for anti-resonant states, and None for continuum states). Return type:str or NoneType

analytic

Returns:Analyticity of the scalar products. Return type:bool

__eq__(other)

Two analytic eigenstates are the same if they share the same wavenumber, potential and Siegert_type.

Parameters:other (object) – Another object Returns:True if both eigenstates are the same. Return type:bool

scal_prod(other, xlim=None)

Note

This is an asbtract method.

Evaluate the scalar product between the state and a test function other. It ensures that the numerical scalar product is computed when the analytical scalar product with test functions is not implemented in the child class.

Parameters:

• other (Function) – Test function.
• xlim (tuple(float, float)) – Bounds of the space grid defining the interval over which the scalar product must be computed.

Returns:

Value of the scalar product of the state with a test function.

Return type:

float or complex

class siegpy.analyticeigenstates.AnalyticSiegert(k, potential, grid, analytic)

Bases: siegpy.analyticeigenstates.AnalyticEigenstate

Class specifying the abstract method allowing to find the type of the analytic eigenstate, in the case it is a Siegert state.

Parameters:

• k (complex) – Wavenumber of the eigenstate.
• potential (Potential) – Potential for which the analytic eigenstate is known.
• grid (list or set or numpy array) – Discretization grid.
• analytic (bool) – If True, the scalar products must be computed analytically.

Raises:

WavenumberError – If the inferred Siegert type is unknown.

_find_Siegert_type(k)

Parameters:k (complex) – Wavenumber of the Siegert state. Returns:The type of the Siegert state, namely:

• 'b' for a bound state
• 'ab' for an anti-bound state
• 'r' for a resonant state
• 'ar' for an anti-resonant state

Return type:str Raises:WavenumberError – If the wavenumber is equal to zero.

class siegpy.analyticeigenstates.AnalyticContinuum(k, potential, grid, analytic)

Bases: siegpy.analyticeigenstates.AnalyticEigenstate

Class specifying the abstract method allowing to find the type of the analytic eigenstate, in the case it is a continuum state.

Parameters:

• k (complex) – Wavenumber of the eigenstate.
• potential (Potential) – Potential for which the analytic eigenstate is known.
• grid (list or set or numpy array) – Discretization grid.
• analytic (bool) – If True, the scalar products must be computed analytically.

Raises:

WavenumberError – If the inferred Siegert type is unknown.

_find_Siegert_type(k)

Parameters:k (float) – Wavenumber of the continuum state. Returns:None, given that a continuum state is not a Siegert state. Return type:NoneType Raises:WavenumberError – If the wavenumber is imaginary.