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 informations

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