Self-consistent-phonon,random phase,and transfer-integral methods for a linear chain with anharmonic potential

The transfer-integral (TI) method, developed especially for hard-core potentials, is tested with anx² + ₃x³ + ₄x⁴ potential by a comparison with other methods: In the harmonic approximation the improvement of the TI method over the self-consistent phonon (SCP) method is about as great as that of the SCP method over the random phase approximation (RPA).