SWPotential

The SWPotential class representing a 1D Square-Well Potential (1DSWP) is defined below.

class siegpy.swpotential.SWPotential(l, V0, grid=None)

Bases: siegpy.functions.Rectangular, siegpy.potential.Potential

A 1D SW potential is nothing but a rectangular function that is considered as a potential. This class therefore inherits from and extends the Rectangular and Potential classes.

A 1D SWP is initialized from a width \(l\) and a depth \(V_0\). If a grid is given, the potential is discretized over this grid.

Parameters:

• l (float) – Width of the potential.
• V0 (float) – Depth of the potential.
• grid (numpy array or list or set) – Discretization grid of the potential (optional).

Raises:

ValueError – If the depth and width of the potential are not strictly positive.

Examples

A SWPotential instance represents nothing but a centered rectangular function with a negative amplitude:

>>> xgrid = [-4, -2, 0, 2, 4]
>>> pot = SWPotential(5, 10, grid=xgrid)
>>> pot.width == 5 and pot.amplitude == -10
True
>>> pot.center == 0 and pot.momentum == 0
True
>>> pot.values
array([  0.+0.j, -10.+0.j, -10.+0.j, -10.+0.j,   0.+0.j])

Rather than dealing with a negative amplitude, the positive depth of the SW potential is mainly used:

>>> pot.depth
10

classmethod from_center_and_width(xc, a, k0=0.0, h=1.0, grid=None)

Class method overriding the inherited siegpy.functions.Rectangular.from_center_and_width() class method.

Parameters:

• xc (float) – Center of the potential (must be 0).
• a (float) – Width of the potential.
• k0 (float) – Initial momentum of the potential (must be 0).
• h (float) – Depth of the potential (default to 1).
• grid (list or numpy array) – Discretization grid (optional).

Returns:

An initialized 1D SW potential.

Return type:

SWPotential

Raises:

ValueError – If the initial momentum or the center is not zero.

Examples

>>> pot = SWPotential.from_center_and_width(0, 5, h=-10)
>>> pot.width == 5 and pot.depth == 10
True

A Potential cannot have a non-zero center nor an initial momentum:

>>> SWPotential.from_center_and_width(2, 5)
Traceback (most recent call last):
ValueError: A SWPotential must be centered.
>>> SWPotential.from_center_and_width(0, 5, k0=1)
Traceback (most recent call last):
ValueError: A SWPotential cannot have an initial momentum.

The same is valid for the from_width_and_center() class method:

>>> SWPotential.from_width_and_center(5, 2)
Traceback (most recent call last):
ValueError: A SWPotential must be centered.
>>> SWPotential.from_width_and_center(5, 0, k0=1)
Traceback (most recent call last):
ValueError: A SWPotential cannot have an initial momentum.

depth

Returns:Depth of the 1D SW potential. Return type:float

__eq__(other)

Parameters:other (object) – Any other object. Returns:True if two SW potentials have the same width and depth. Return type:bool

Examples

>>> SWPotential(5, 10) == SWPotential(5, 10, grid=[-1, 0, 1])
True
>>> SWPotential(5, 10) == Potential([-1, 0, 1], [-10, -10, -10])
False

__add__(other)

Override of the addition, taking care of the case of the addition of two SW potentials with the same width.

Parameters:other (Potential) – Another potential Returns:The sum of both potentials. Return type:Potential or Function

Examples

The addition of two Square-Well potentials of the same width keeps the analyticity:

>>> xgrid = [-4, -2, 0, 2, 4]
>>> pot = SWPotential(5, 10, grid=xgrid)
>>> pot += SWPotential(5, 5)
>>> isinstance(pot, SWPotential)
True
>>> pot.amplitude == -15 and pot.depth == 15 and pot.width == 5
True
>>> pot.values
array([  0.+0.j, -15.+0.j, -15.+0.j, -15.+0.j,   0.+0.j])

In any other case, the analyticity is lost, but the result still is a potential:

>>> pot += Potential(xgrid, [5, 5, 5, 5, 5])
>>> isinstance(pot, SWPotential)
False
>>> isinstance(pot, Potential)
True
>>> pot.values
array([  5.+0.j, -10.+0.j, -10.+0.j, -10.+0.j,   5.+0.j])

complex_scaled_values(coord_map)

Evaluates the complex scaled SW potential. It actually amounts to the potential without complex scaling, as the Square-Well Potential is a piecewise function (the complex scaling has no effect on it).

Parameters:coord_map (CoordMap) – Coordinate mapping. Returns:Complex scaled values of the potential. Return type:numpy array