Statistical Mechanics – MEGR 7090/8090
Lecture Notes
1) Introduction; overview of macroscopic equilibrium thermo: lecture1-macrothermo-review
2) Derivation of Gibb’s relations, Maxwell relations, generalized du: lecture1-notes
3) More macroscopic thermo: lect2-macro-review-cont
4) Fundamental postulates, part 1: lecture2-part2-notes
5) Fundamental postulates, part 2: lecture2-aside-estimate-probability-1-ptcl-total-energy-5
6) Fundamental postulates, part 3: lecture3-generallization-fund-postulates-n-indep-particle-systems-6
7) Boltzmann’s attempt to connect micro- and macroscale equilibrium thermo: lecture2-part1-notes-7
8) Derivation of Boltzmann entropy relation (ca 2015): lec4-derivation-boltzmann-relation-8
9) Relation between k and universal gas constant; rough repeat of Reif’s degree-of-freedom argument: lec4-2015-connectktor-9
10) Rough rederivation of Reif’s DoF argument; rough alternate derivation of number of quantum states in an N-particle ideal gas: lec4-rough-2015-reifdofpluspathrianoofstatesigas-11
11) Quantum mechanics overview, part 1: lecture-4-quantum-mech-overview-part1-12
12) Quantum mechanics overview, part 2 (rough): lecture-4-quantum-mech-overview-rough-version-part1-13
13) Ensemble overview; QM recipe; when to choose quantum versus classical model: ensemble-method-overview-quantum-mech-recipe-thermal-wavelength-2015-14
14) Derivation of canonical distribution: canonical-distbn-derivation-2015-16
15) Rederivation of canonical distribution; overview of phase space of N-particle system: lec9-2015-phase-space-deriavtion1-canonical-density-fn-17
16) Improved derivation of canonical distribution: canon-distbn-good-dervn-version1-2015-18
17) Derivation of A=kTlnQ; G=μN; S=k ∑ plnp; S = k ln Ω: dervnaktlnq-gmun-sksumprlnpr-20
18) Degenerate states; example degeneracy estimate for single particle in aa box (not in Pathria): dervn-canon-dist-degenerate-energy-levels-22
19) Rigorous derivation of microcanonical distribution (not in Pathria): rigorous-dervn-microcanonical-distribution-22
20) On the equivalence of state density, g(E), and Ω: eqivalence-of-ge-omega-23
19) Rigorous derivation of microcanonical distribution (not in Pathria): rigorous-dervn-microcanonical-distribution-22
20) Example calculation of g(E) for classical ideal gas (Laplace transform inversion): laplace-inversion-ex-ge-aside-quantum-conversion-factor-24
21) Example calculation of partition function, Q, for classical ideal gas: example-calc-partition-fn-classical-ideal-gas-25
22) Derivation of Liouville theorem: dervn-continuum-cons-eqns-via-kirkwood-liouville-theorem-26
23) Interacting particle systems; molecular-scale conservation laws: interacting-classical-particle-systems-molecular-scale-conservation-laws-part1-27
24) Molecular-scale ensemble-averaged momentum equation: derivn-ensemble-avg-molecular-scale-momentum-eqn-28
25) Appendix 1: Quantum energy states of a free particle in a box: lecture-5-quantum-energy-lstates-free-ptcl-29
26) Appendix 2: Details underlying Pathria’s derivation of quantum phase space volume: lecture-11-dervn-of-no-quantum-states-per-unit-vol-phase-space-30
27) Appendix 3: Combinatorics warm-up: combinatorics-1-lec5-2015-31
28) Appendix 4: X and P bases in quantum mechanics: lecture-18-pt1-x-and-p-bases-in-qm-32
Send email to rkeanini@uncc.edu