1. 4/24/2015PHY 752 Spring 2015 -- 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

2. 4/24/2015PHY 752 Spring 2015 -- Lecture 362

3. 4/24/2015PHY 752 Spring 2015 -- Lecture 363

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

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

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

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

8. PHY 712 Spring 2015 -- Lecture 368 Evaluation of Kramer’s Kronig transform using Mathematica (with help from Professor Cook)

9. 04/24/2015PHY 712 Spring 2015 -- Lecture 369 Another example

10. 04/24/2015PHY 712 Spring 2015 -- Lecture 3610 Some equations worth remembering --

11. 4/24/2015PHY 752 Spring 2015 -- Lecture 3611

12. 4/24/2015PHY 752 Spring 2015 -- Lecture 3612 a1a1 a2a2 a3a3 Bravais lattice vectors: Distance between diffracting planes

13. 4/24/2015PHY 752 Spring 2015 -- Lecture 3613 Bragg diffraction incident beam defracted beam In terms of wave vectors k inc k scat kk 

14. 4/24/2015PHY 752 Spring 2015 -- 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

15. 4/24/2015PHY 752 Spring 2015 -- 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, 165107 (2003)Phys. Rev. B 68, 165107 (2003)

16. 4/24/2015PHY 752 Spring 2015 -- Lecture 3616 Partial densities of states FePO 4 LiFePO 4

17. 4/24/2015PHY 752 Spring 2015 -- Lecture 3617

18. 4/24/2015PHY 752 Spring 2015 -- Lecture 3618