\hat{I}-\frac{i}{\hbar}t\hat{H}+\frac{i}{\hbar}t\hat{H}+\sum_i \lambda_i \hat{a}_i+\frac{i}{\hbar}t\hat{H}\sum_i \lambda_i \hat{a}_i-\sum_i \lambda_i \hat{a}_i\frac{i}{\hbar}t\hat{H}+\ldots=\hat{I}