Title: Summary Perturbation Theory

Choose the correct statement.

- Perturbation theory is used when we know the exact solution of the Schrödinger equation for a Hamiltonian that is close to the true Hamiltonian. We can then predict how the true wavefunction and energy differ from the ones we can solve. (correct)
- Perturbation theory is used when we cannot solve the Schrödinger equation exactly. We can guess a wavefunction, and Perturbation theory tells us how good our guess is.

- Perturbation theory is used to understand why some materials are ferroelectric. (correct)
- Perturbation theory is used to understand why some materials are ferromagnetic.

- The ferroelectric distortion is favoured with respect to the paraelectric structure if it presents a lower energy. (correct)
- The ferroelectric distortion is favoured with respect to the paraelectric structure if it presents a higher energy.

- The first-order correction to the energy is always zero by symmetry in the case of a ferroelectric distortion. (correct)
- The first-order correction to the energy is non-zero by symmetry in the case of a ferroelectric distortion.

- The Second-Order Jahn-Teller effect is determined by the second-order energy terms in perturbation theory. (correct)
- The Second-Order Jahn-Teller effect is determined by the first-order energy term in perturbation theory.

- The sign of the second-order term determines whether or not the ferroelectric distortion will occur. (correct)
- The magnitude of the second-order term determines whether or not the ferroelectric distortion will occur.

- The left term takes into account the Coulomb repulsion that arises when atoms get closer, and therefore it disfavours ferroelectricity. (correct)
- The left term takes into account the Coulomb attraction that arises when atoms get closer, and therefore it favours ferroelectricity.

- The right term describes the rehybridization of the electron clouds in response to the ionic displacement. (correct)
- The right term describes the Jahn-Teller distortion in response to the ionic displacement.

- The right term will be the largest for the lowest excited state, for which the denominator is the smallest. (correct)
- The right term will be the smallest for the lowest excited state, for which the denominator is the smallest.

- We can evaluate the right term using symmetry arguments, by looking at the symmetry of the top of the valence band and the bottom of the conduction band. If one of these is odd and the other one is even, the right term will be non-zero and therefore a ferroelectric distortion will be favoured. (correct)
- We can evaluate the right term using symmetry arguments, by looking at the symmetry of the top of the valence band and the bottom of the conduction band. If they are both odd or both even, the right term will be non-zero and therefore a ferroelectric distortion will be favoured.