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 projet on github.