run_numerov_integration
- ryd_numerov.radial.run_numerov_integration(x_start, x_stop, dx, y0, y1, g_list, x_min, verbose=False)[source]
Run the Numerov integration algorithm.
This means, run the Numerov method, which is defined for
\[\frac{d^2}{dx^2} y(x) = - g(x) y(x)\]as
\[y_{n+1} (1 + \frac{h^2}{12} g_{n+1}) = 2 y_n (1 - \frac{5 h^2}{12} g_n) - y_{n-1} (1 + \frac{h^2}{12} g_{n-1})\]- Parameters:
x_start (
float) – The initial value of the x-coordinate.x_stop (
float) – The final value of the x-coordinate.dx (
float) – The step size of the integration (can be negative).y0 (
float) – The initial value of the function y(x) at the first (or last if run_backward) x-value.y1 (
float) – The initial value of the function y(x) at the second (or second last if run_backward) x-value.g_list (
Union[Sequence[float],ndarray[tuple[int,...],dtype[Any]]]) – A list of the values of the function g(x) at each x-value.x_min (
float) – The minimum value of the x-coordinate, until which the integration should be run. Once the x-value reaches x_min, we check if the function y(x) is zero and stop the integration.verbose (
bool) – If True, print additional information.
- Returns:
A list of the values of the function y(x) at each x-value
- Return type:
y_list