1/28/2015PHY 7r2 Spring 2015 -- Lecture 61 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 6: Reading: Chapter 6 in MPM; Electronic.

Slides:



Advertisements
Similar presentations
The Quantized Free Electron Theory Energy E Spatial coordinate x Nucleus with localized core electrons Jellium model: electrons shield potential.
Advertisements

9/22/2013PHY 711 Fall Lecture 121 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 12: Continue reading.
1 Lecture 5 The grand canonical ensemble. Density and energy fluctuations in the grand canonical ensemble: correspondence with other ensembles. Fermi-Dirac.
1/14/2015PHY 752 Spring Lecture 21 PHY 752 Electrodynamics 9-9:50 AM MWF Olin 107 Plan for Lecture 2: Reading: Chapter 1 & 2 in MPM; Crystal structures.
Quantum Mechanics Discussion. Quantum Mechanics: The Schrödinger Equation (time independent)! Hψ = Eψ A differential (operator) eigenvalue equation H.
Electrons in metals Energy E Spatial coordinate x Nucleus with localized core electrons Jellium model: electrons shield potential to a large extent.
MSEG 803 Equilibria in Material Systems 10: Heat Capacity of Materials Prof. Juejun (JJ) Hu
Thermo & Stat Mech - Spring 2006 Class 22 1 Thermodynamics and Statistical Mechanics Fermi-Dirac Statistics.
1/12/2015PHY 752 Spring Lecture 11 PHY 752 Electrodynamics 11-11:50 AM MWF Olin 107 Plan for Lecture 1: Reading: Chapters 1-2 in Marder’s text.
02/03/2014PHY 712 Spring Lecture 81 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 8: Start reading Chapter 4 Multipole moment.
3/30/2015PHY 752 Spring Lecture 261 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 26:  Chap. 19 in Marder  Properties.
4/15/2015PHY 752 Spring Lecture 321 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 32:  The Hubbard model  Motivation.
02/19/2014PHY 712 Spring Lecture 151 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 15: Finish reading Chapter 6 1.Some details.
02/18/2015PHY 712 Spring Lecture 151 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 15: Finish reading Chapter 6 1.Some details.
Exam I results.
Specific Heat of Solids Quantum Size Effect on the Specific Heat Electrical and Thermal Conductivities of Solids Thermoelectricity Classical Size Effect.
Lecture 21. Grand canonical ensemble (Ch. 7)
9/11/2013PHY 711 Fall Lecture 71 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 7: Continue reading.
The Ideal Monatomic Gas. Canonical ensemble: N, V, T 2.
9/24/2014PHY 711 Fall Lecture 131 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 13: Finish reading.
2/20/2014PHY 770 Spring Lecture 121 PHY Statistical Mechanics 12:00-1:45 PM TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course.
9/28/2015PHY 711 Fall Lecture 151 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 15: Continue reading.
3/27/2015PHY 752 Spring Lecture 251 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 25:  Chap. 18 & 19 in Marder  Impurity.
2/18/2014PHY 770 Spring Lecture PHY Statistical Mechanics 11 AM – 12:15 & 12:30-1:45 PM TR Olin 107 Instructor: Natalie Holzwarth.
Chapter 7 Bose and Fermi statistics. §7-1 The statistical expressions of thermodynamic quantities 1 、 Bose systems: Define a macrocanonical partition.
3/23/2015PHY 752 Spring Lecture 231 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 23:  Transport phenomena and Fermi liquid.
2/16/2015PHY 752 Spring Lecture 141 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 14: Reading: Chapter 10 in MPM Numerical.
1/26/2015PHY 7r2 Spring Lecture 51 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 5: Reading: Chapter 7.3 in MPM; Brief.
2/26/2014PHY 770 Spring Lecture 131 PHY Statistical Mechanics 12:00 * -1:45 PM TR Olin 107 Instructor: Natalie Holzwarth (Olin 300) Course.
4/6/2015PHY 752 Spring Lecture 281 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 28:  Chap. 21 in Marder & pdf file from.
2/09/2015PHY 752 Spring Lecture 111 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 11: Reading: Chapter 9 in MPM Approximations.
9/19/2012PHY 711 Fall Lecture 101 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 10: Continue reading.
2/18/2015PHY 752 Spring Lecture 151 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 15: Reading: Chapter 10 in MPM Numerical.
11/22/2013PHY 711 Fall Lecture 341 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 34: Chapter 11.
3/25/2015PHY 752 Spring Lecture 241 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 23:  Transport phenomena – Chap. 17.
2/06/2015PHY 752 Spring Lecture 101 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 10: Reading: Chapter in MPM;
Thermal Conduction in Metals and Alloys Classical Approach From the kinetic theory of gases ) where, l is mean free path.
2/11/2015PHY 752 Spring Lecture 121 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 12: Reading: Chapter 9 in MPM Approximations.
02/13/2015PHY 712 Spring Lecture 131 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 13: Continue reading Chapter 5 1.Hyperfine.
Group theory and intrinsic spin; specifically, s=1/2
Chapter 6 Applications of
PHY 752 Solid State Physics Review: Chapters 1-6 in GGGPP
PHY 752 Solid State Physics
16 Heat Capacity.
PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107
PHY 745 Group Theory 11-11:50 AM MWF Olin 102 Plan for Lecture 23:
PHY 712 Electrodynamics 11-11:50 AM MWF Olin 107 Plan for Lecture 14:
Symmetry of lattice vibrations
PHY 752 Solid State Physics Superconductivity (Chap. 18 in GGGPP)
PHY 752 Solid State Physics
16 Heat Capacity.
Quantum states of a diatomic molecule H2+ with stationary nuclei
PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 14:
Chap. 17 in Shankar: Magnetic field effects – atoms, charged particles
PHY 752 Solid State Physics Plan for Lecture 28: Chap. 9 of GGGPP
Quantum Chemistry / Quantum Mechanics
PHY 752 Solid State Physics
Group theory and intrinsic spin; specifically, s=1/2
Chap. 20 in Shankar: The Dirac equation for a hydrogen atom
PHY 752 Solid State Physics
Group theory for the periodic lattice
PHY 752 Solid State Physics
“Addition” of angular momenta – Chap. 15
PHY 752 Solid State Physics
“Addition” of angular momenta – Chap. 15
PHY 752 Solid State Physics
PHY 752 Solid State Physics Plan for Lecture 29: Chap. 9 of GGGPP
PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 13:
PHY 752 Solid State Physics 11-11:50 AM MWF Olin 103
Chap. 19 in Shankar: Scattering theory
Presentation transcript:

1/28/2015PHY 7r2 Spring Lecture 61 PHY 752 Solid State Physics 11-11:50 AM MWF Olin 107 Plan for Lecture 6: Reading: Chapter 6 in MPM; Electronic Structure 1.Independent electron models 2.Free electron gas 3.Densities of states 4.Statistical mechanics of non-interacting electrons

1/28/2015PHY 7r2 Spring Lecture 62

1/28/2015PHY 7r2 Spring Lecture 63

1/28/2015PHY 7r2 Spring Lecture 64 Born-Oppenheimer approximation Born & Huang, Dynamical Theory of Crystal Lattices, Oxford (1954) Electronic coordinates Atomic coordinates Quantum Theory of materials

1/28/2015PHY 7r2 Spring Lecture 65 Quantum Theory of materials -- continued Effective nuclear interaction provided by electrons (Often treated classically)

1/28/2015PHY 7r2 Spring Lecture 66 Terms neglected in Born-Oppenheimer approximation

1/28/2015PHY 7r2 Spring Lecture 67 First consider electronic Hamiltonian Replace by “jellium” Independent electron contributions

1/28/2015PHY 7r2 Spring Lecture 68 Treatment of each electron (Fermi particle) in the jellium model Note: This and following slides taken from Marder’s text

1/28/2015PHY 7r2 Spring Lecture 69 Enumerating the independent electron states by summing over k:

1/28/2015PHY 7r2 Spring Lecture 610 Enumerating the independent electron states by summing over k – continued: Note: Each spatial state has a spin degeneracy of 2.

1/28/2015PHY 7r2 Spring Lecture 611 Enumerating the independent electron states by summing over k – continued for :

1/28/2015PHY 7r2 Spring Lecture 612 Enumerating the independent electron states by summing over k – continued for :

1/28/2015PHY 7r2 Spring Lecture 613 Enumerating the independent electron states by summing over k – continued for :

1/28/2015PHY 7r2 Spring Lecture 614 Note: Previous results are special to a 3-dimensional jellium system where the electronic states are related to the wavevectors according to For your homework problem, you will consider a 2- dimensional jellium system with two different dispersions: E(k)=Xk 2 and E(k)=Xk.

1/28/2015PHY 7r2 Spring Lecture 615 Statistical mechanics of free Fermi gas in terms of “grand” partition function

1/28/2015PHY 7r2 Spring Lecture 616 “Grand” potential

1/28/2015PHY 7r2 Spring Lecture 617

1/28/2015PHY 7r2 Spring Lecture 618

1/28/2015PHY 7r2 Spring Lecture 619 Jellium analysis of some metals

1/28/2015PHY 7r2 Spring Lecture 620 How well does the jellium model work – analysis of electronic contribution to specific heat First consider the following trick:

1/28/2015PHY 7r2 Spring Lecture 621

1/28/2015PHY 7r2 Spring Lecture 622

1/28/2015PHY 7r2 Spring Lecture 623

1/28/2015PHY 7r2 Spring Lecture 624 Specific heat table from Marder’s text:

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.