In this work, we study the a posteriori error estimation for time-splitting spectral approximations of the two-dimensional semiclassical Schr\\odinger equation. A Fourier spectral discretization in space combined with Lie or Strang splitting schemes in time is used to resolve highly oscillatory wave functions in the semiclassical regime. A residual-based framework is developed to quantify the accuracy of the numerical solutions.
To validate the approach, we construct the 2D coherent state exact solutions with the quadratic isotropic potentials, and compare them with the Lie or Strang numerical approximations, demonstrating the convergence rate of the methods, and verifying that the a posteriori estimator provides a sharp upper bound for the true error. This provides a foundation for extending the a posteriori error analysis to two-level Schr\\odinger systems with conical crossings.