# 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.