Diabatic process: Rapidly changing conditions prevent the system from adapting its configuration during the process, hence the spatial probability density remains unchanged.
For a truly adiabatic process we require \scriptstyle{\tau \rightarrow \infty}; in this case the final state \scriptstyle{\psi(x,t_1)} will be an eigenstate of the final Hamiltonian \scriptstyle{\hat{H}(t_1)}, with a modified configuration: .