"""Contains some pre-defined electron-electron interations"""
import numpy as np
__all__ = [
"softened_interaction",
"softened_interaction_alternative",
]
[docs]def softened_interaction(x: np.ndarray, strength: float = 1.0, softening: float = 1.0) -> np.ndarray:
r"""
Constructs the softened interaction potential.
.. math:: v_\mathrm{int}(x,x') = \frac{s}{|x-x'| + a}
| Args:
| x: np.ndarray, x grid.
| strength: float, Strength of the interaction .. math:: s. (default = 1.0)
| softening: float, Softening parameter of the interaction .. math:: a. (default = 1.0)
| Returns:
| v_int: np.ndarray, Softened interaction potential on x grid of the System.
"""
v_int = np.zeros((x.shape[0], x.shape[0]), dtype="float")
for i in range(x.shape[0]):
for j in range(x.shape[0]):
v_int[i, j] = strength / (abs(x[i] - x[j]) + softening)
return v_int
[docs]def softened_interaction_alternative(x: np.ndarray, strength: float = 1.0, softening: float = 1.0) -> np.ndarray:
r"""
Constructs the alternative softened interaction potential.
.. math:: v_\mathrm{int}(x,x') = \frac{s}{{(\sqrt{x-x'} + a)}^{2}}
| Args:
| x: np.ndarray, x grid.
| strength: float, Strength of the interaction .. math:: s. (default = 1.0)
| softening: float, Softening parameter of the interaction .. math:: a. (default = 1.0)
| Returns:
| v_int: np.ndarray, Softened interaction potential on x grid of the System.
"""
v_int = np.zeros((x.shape[0], x.shape[0]), dtype="float")
for i in range(x.shape[0]):
for j in range(x.shape[0]):
v_int[i, j] = strength / np.sqrt((x[i] - x[j]) ** 2 + softening)
return v_int