code: def verlet_integrator(
      position: np.ndarray,
      momentum: np.ndarray,
      time_step: float,
      state_derivatives_fn: StateDerivativesFnType,
  ) -> Tuple[np.ndarray, np.ndarray]:
      """Implementation of Verlet integrator (see `abstract_integrator`)."""
  
      _, dmomentum_dt = state_derivatives_fn(position, momentum)
      aux_momentum = momentum + dmomentum_dt * time_step / 2
  
      dposition_dt, _ = state_derivatives_fn(position, aux_momentum)
      next_position = position + dposition_dt * time_step
  
      _, dmomentum_dt = state_derivatives_fn(
          next_position, aux_momentum
      )
      next_momentum = aux_momentum + dmomentum_dt * time_step / 2
  
      return next_position, next_momentum
  
imports: import functools
  from typing import Tuple, Callable
  from absl import app
  from frozendict import frozendict
  import jax
  import jax.numpy
  import jraph
  import matplotlib.pyplot
  import numpy
label_desc: Use image node_id 12 for calling a global function with example usage: verlet_integrator(position, momentum, time_step, state_derivatives_fn) and returns: next_position,  next_momentum