Figure 5: Expectation values of the Hamiltonian and their time averages for toward the end of the time integration. Lower: state. Upper: state. These energies, especially for the state, have some numerical noise (high-frequency hair superimposed on the wave oscillation), but nevertheless the time averages at maximum time agree well with the time-independent results, which are −1.174 and −0.7842 for the and states, respectively.