It provides one possible visualization tool, usually in the form of the transition density, T (r) ≡ T (r, r). Often, Eq. (2.2) is simplified by invoking the Tamm-Dancoff approximation (TDA), in which the de-excitation amplitudes y ia are neglected. These amplitudes arise naturally in the equation-of-motion formalism for the one-particle density matrix, yet in molecular TD-DFT calculations they are typically ∼ 100× smaller than the largest x ia . (This this may not always be the case for solids. ) The matrix B is absent from the resulting TDA eigenvalue problem, which is simply Ax = ωx .