2D Schrödinger equation simulation

Description

This node is an implementation of a 2D simulation of the Schrödinger equation.

Important to know:

The node outputs the state of the simulation at the current frame.
All the simulation data are stored for each frame. Whenever a parameter changes, all the data for the current simulation are deleted.
The simulation depends on all the previous frames. So if you suddenly ask for a frame that was not already computed and that is "far" from the last computed frame, the simulation can take a few seconds to compute this frame (since it has to compute all the previous frames).

Outputs

Output: 2d grid of complex numbers. The grid is formatted this way:

[z_11, ..., z_1n, z_21, ..., z_2n, ..., z_n1, ..., z_nn]

 ^ ----------- ^, ...   ..., ...   ..., ^ ----------- ^

    n numbers        ...        ...        n numbers

This output is fully equivalent to a n*n matrix.

Offset: size of the 2d grid.

This offset can help you to naviguate through all the data as if it was a matrix.

Inputs

Time-related parameters
- Frame rate: frame rate of the simulation.
- Duration: duration of the simulation.
- Δt: simulation time spent for each second of animation.
Precision-related parameters.
- Dimension: size of the 2d grid.
- Scale: scale of the simulation.
Wave packet-related parameters
- Center: starting position of the wave packet.
- Number of waves: number of waves that compose the wave packet.
- Spreading: spreading of the wave packet.
Potential: boolean expression of the potential (in function of x and y).
Obstacle: boolean expression of the obstacle.s (in function of x and y).

More information

This node is made possible thanks to Azercoco and his implementation of the simulation, see the project on github.