== Lecture Notes == * '''Lecture 21''', ~-May 21-~: <> {{{#!wiki comment * <> Page 2, top, “Debye → de Broglie” (Thanks, PM!)—~-''<>''-~ * <> Comments on the van der Waals equation of state (pages 7-8).—~-''<>''-~ }}} * '''Lecture 20''', ~-Reading-~: <> * '''Lecture 19''', ~-June 5-~: <> * '''Lecture 18''', ~-June 3-~: <> * '''Lecture 17''', ~-May 29-~: <> {{{#!wiki comment * <> The small last paragraph of 17.3 is now removed. There was an error in the argument, while the conclusion for the DMFT was good (just cannot be inferred this way).—~-''<>''-~ }}} * '''Lecture 16''', ~-May 27-~: <> {{{#!wiki comment * <> Footnote 1 removed. Footnote 1 (old footnote 2) is rebuffed with details added (Bragg-Williams free energy is derived in it). Footnote 2 refers to footnote 1.—~-''<>''-~ }}} * '''Lecture 15''', ~-May 22-~: <> {{{#!wiki comment * <> Eq. 15.25, negative sign, removed. (Thanks, PM!)—~-''<>''-~ }}} * '''Lecture 14''', ~-May 20-~: <> {{{#!wiki comment * <> A new footnote (2) regarding the symbol $n$.—~-''<>''-~ * <> $z-1 \rightarrow 1-z$ in page 8, in the first part of proof.—~-''<>''-~ }}} * '''Lecture 13''', ~-May 15-~: <> * '''Lecture 12''', ~-May 13-~: <> {{{#!wiki comment * <> A box, and more comments near the end (Eq. 12.50).—~-''<>''-~ }}} * '''Lecture 11''', ~-May 8-~: See LN 10. We also discussed a very important qualitative way to quickly re-derive the Debye $T^3$ law (<>). We also discussed how the $T^3$ law would change if we had ferromagnetic spin waves ($\omega \propto k^2$, at long wave length). We derived the answer that $C_V \propto T^{3/2}$. For experimental data on ferromagnetic materials (including EuB$_6$, mentioned in class—''not'' a clear-cut case to demonstrate the $T^{3/2}$ law, I think), check the literature: <> or <>, for example. * '''Lecture 10''', ~-May 6-~: <> {{{#!wiki comment * <> A new footnote (7).—~-''<>''-~ * <> Eq. 10.15, the $\hbar$ factor is dropped. Eqs. 10.24 and 25 are re-written. The previous version of these two equations were ''not'' applicable to all particles.—~-''<>''-~ }}} * '''Lecture 9''', ~-May 1-~: <> {{{#!wiki comment * <> Two section numbers in footnote 8.—~-''<>''-~ * <> A box in page 6. Section 9.3.3. Both of these additions were discussed, in one form or another, in lectures. Footnote 20. (Also, an old footnote (footnote 10, I think) is deleted, as it was found to be unnecessary.)—~-''<>''-~ }}} * '''Lecture 8''', ~-Apr 29-~: <> {{{#!wiki comment * <> Discussions in page 14 have been simplified a bit, and then a question has been added.—~-''<>''-~ }}} * '''Lecture 7''', ~-Apr 24-~: <> {{{#!wiki comment * <> Footnote 5, page 7.—~-''<>''-~ * <> Added some more comments to item 4 in page 8.—~-''<>''-~ * <> Key notes added after that ''super''-important table in page 7.—~-''<>''-~ * <> The symbol change for microstate (from a left-leaning "mu" to a "mu" with a wavy decorator on lower left).—~-''<>''-~ }}} * '''Lecture 6''', ~-Apr 22-~: <> {{{#!wiki comment * <> The symbol change for microstate just like for LN 7.—~-''<>''-~ }}} * '''Lecture 5''', ~-Apr 17-~: <> * '''Lecture 4''', ~-Apr 15-~: <> {{{#!wiki comment * <> Definition of correlation and covariance (Eq. 4.13) has a new comment below it. Also, the word '''covariance''' is mentioned.—~-''<>''-~ * <> Bayesian inference is upgraded from footnote to sub-section (page 3).—~-''<>''-~ }}} * '''Lecture 3''', ~-Apr 10-~: <> {{{#!wiki comment * <> Eq. 3.3: $\langle p(x) \rangle \rightarrow \langle e^{-ikx} \rangle$. Eq. 3.12: missing $\langle x \rangle_c$ put back for the 4th term (thanks DH, for spotting this typo!).—~-''<>''-~ * <> Line 2 of Section 3.2.2: $/N \rightarrow /\sqrt{N}$.—~-''<>''-~ }}} * '''Lecture 2''', ~-Apr 8-~: <> {{{#!wiki comment * <> Discussion in Section 2.3 is beefed up a bit (new stuff added here and there). In particular, paragraph 3 (a new one) in page 10 is highly recommended for your careful consumption. In Eq. 2.39 and around it, notation change: $T_0, J_0, S_0 \rightarrow T_R, J_R, S_R$ (better coherence with contents of Section 2.3).—~-''<>''-~ * <> Lots of little corrections/improvement/clarifications were added in pages 8 through 17. Please, update! Two most important changes: (i) page 8, Gibbs free energy, the $dG$ expression was jumbled--corrected. (ii) on the same page, $\delta$ is now replaced by $d$.—~-''<>''-~ }}} * '''Lecture 1''', ~-Apr 1-~: <> {{{#!wiki comment * <> Some comments are added after Eq. 1.2. Thanks PM, whose question prompted this addition!—~-''<>''-~ }}}