4/24/2015PHY 752 Spring Lecture 361 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 36: Review  Comment on Kramers-Kronig transforms  Some equations worth knowing  Course assessment forms

4/24/2015PHY 752 Spring Lecture 362

4/24/2015PHY 752 Spring Lecture 363

Review topic – analytic properties of dielectric function Kramers-Kronig transform – for dielectric function: PHY 712 Spring Lecture 36404/24/2015

Practical evaluation of Kramers-Kronig relation PHY 712 Spring Lecture 36504/24/2015

Practical evaluation of Kramers-Kronig relation PHY 712 Spring Lecture 36604/24/2015

Evaluation of singular integral numerically: PHY 712 Spring Lecture 36704/24/2015

PHY 712 Spring Lecture 368 Evaluation of Kramer’s Kronig transform using Mathematica (with help from Professor Cook)

04/24/2015PHY 712 Spring Lecture 369 Another example

04/24/2015PHY 712 Spring Lecture 3610 Some equations worth remembering --

4/24/2015PHY 752 Spring Lecture 3611

4/24/2015PHY 752 Spring Lecture 3612 a1a1 a2a2 a3a3 Bravais lattice vectors: Distance between diffracting planes

4/24/2015PHY 752 Spring Lecture 3613 Bragg diffraction incident beam defracted beam In terms of wave vectors k inc k scat kk 

4/24/2015PHY 752 Spring Lecture 3614 periodic function Single particle wavefunction in a periodic system Wannier representation of electronic states -- continued Comment: Wannier functions are not unique since the the Bloch function may be multiplied by a k-dependent phase, which may generate a different function W n (r-T). Eigenfunctions of the periodic Hamiltonian are Bloch states with eigenvalues E nk and

4/24/2015PHY 752 Spring Lecture 3615 Understanding band structures --- Example of LiFePO 4 and FePO 4 Electronic structures of FePO 4, LiFePO 4, and related materials Ping Tang and N. A. W. Holzwarth -- Phys. Rev. B 68, (2003)Phys. Rev. B 68, (2003)

4/24/2015PHY 752 Spring Lecture 3616 Partial densities of states FePO 4 LiFePO 4

4/24/2015PHY 752 Spring Lecture 3617

4/24/2015PHY 752 Spring Lecture 3618