Time Evolution

Allows for numerical time-evolution of single-particle wave functions in arbitrary (time-dependent or -independent) potentials. 

Input

  • $\psi$: State - The initial state that will be evolved.
  • H: Hamiltonian - The Hamiltonian that will be used to evolve the state.
  • dt: Scalar - The time step size.
  • T: Scalar - The total time.

Output

  • $\psi$: State - The evolved state.
  • t: Time - The current time.

Content

This node is comparatively complicated. It works similarly to the Time Dimension in that it does not update when its inputs get updated, but only when the start-button is pressed. On each step it will take the state and numerically solve the schroedinger-equation for the timestep, emitting the updated state and the corresponding updated time. Note, that the Hamiltonian is allowed to be updated between steps, allowing evolution in time-dependent potentials. The time-dependent potential should use the t-output of this node as its input in that case. This is the only place in the composer where nodes are allowed to be connected in a loop! 

In the beginning (or when the reset-button is pressed), the state is set to the input-state. 

Example