PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 8:

Slides:

Advertisements

Similar presentations

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.

Advertisements

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.

01/31/2014PHY 712 Spring Lecture 71 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 7: Start reading Chapter 3 Solution of Poisson.

3. 3 Separation of Variables We seek a solution of the form Cartesian coordinatesCylindrical coordinates Spherical coordinates Not always possible! Usually.

1/21/2015PHY 712 Spring Lecture 31 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 3: Reading: Chapter 1 in JDJ 1.Review of electrostatics.

1 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 35: Comments and problem solving advice:  Comment about PHY 712 final  General review.

02/05/2014PHY 712 Spring Lecture 91 PHY 712 Electrodynamics 11-11:50 AM MWF Olin 107 Plan for Lecture 9: Continue reading Chapter 4 Dipolar fields.

§3.4. 1–3 Multipole expansion Christopher Crawford PHY

03/21/2014PHY 712 Spring Lecture 211 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 21: Continue reading Chap. 9 A.Electromagnetic.

02/07/2014PHY 712 Spring Lecture 101 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 10: Complete reading of Chapter 4 A.Microscopic.

03/20/2015PHY 712 Spring Lecture 221 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 22: Start reading Chap. 9 A.Electromagnetic.

03/23/2015PHY 712 Spring Lecture 231 PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 23: Continue reading Chap. 9 & 10 A.Electromagnetic.

Multipole Moments Section 41. Expand potential  in powers of 1/R 0.

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.

1 PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 29: Start reading Chap. 15 – Radiation from collisions of charged particles 1.Overview.

PHY 711 Classical Mechanics and Mathematical Methods

Group properties of atomic orbitals and crystals

Group theory and intrinsic spin; specifically, s=1/2

PHY 711 Classical Mechanics and Mathematical Methods

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 6:

System of charges in an external field

PHY 752 Solid State Physics

PHY 752 Solid State Physics

PHY 752 Solid State Physics 11-11:50 AM MWF Olin 103

PHY 752 Solid State Physics

Introduction to groups having infinite dimension

Radiation from collisions of charged particles

PHY 712 Electrodynamics 11-11:50 AM MWF Olin 107 Plan for Lecture 14:

§3.4.1–3 Multipole expansion

Christopher Crawford PHY

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 25:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 1:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 9:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 12:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 9:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 3:

Radiation from collisions of charged particles

PHY 741 Quantum Mechanics 12-12:50 PM MWF Olin 103

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 14:

Finish reading Chapter 6

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 11:

PHY 711 Classical Mechanics and Mathematical Methods

PHY 752 Solid State Physics Inhomogeneous semiconductors

Group theory and intrinsic spin; specifically, s=1/2

Special Topics in Electrodynamics:

Chap. 20 in Shankar: The Dirac equation for a hydrogen atom

Electromagnetic waves due to specific sources

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 23:

Reading: Chapter in JDJ

PHY 711 Classical Mechanics and Mathematical Methods

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 6:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 26:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 1:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 7:

PHY 711 Classical Mechanics and Mathematical Methods

PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 22:

PHY 752 Solid State Physics 11-11:50 AM MWF Olin 103

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103 Plan for Lecture 10:

Space group properties

PHY 752 Solid State Physics

Review Chapter 1-8 in Jackson

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 3:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 11:

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

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 2:

Radiation from collisions of charged particles

Review of electrodynamics

Finish reading Chapter 6

Presentation transcript:

PHY 712 Electrodynamics 9-9:50 AM MWF Olin 105 Plan for Lecture 8: Start reading Chapter 4 Multipole moment expansion of electrostatic potential – Spherical coordinates Cartesian coordinates 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Poisson and Laplace equation in spherical polar coordinates http://www.uic.edu/classes/eecs/eecs520/textbook/node32.html 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Poisson and Laplace equation in spherical polar coordinates -- continued 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Properties of spherical harmonic functions 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Legendre and Associated Legendre functions 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Useful identity: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Some spherical harmonic functions: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Example: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Example: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Example -- continued: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Example -- continued: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Notion of multipole moment: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Significance of multipole moments qlm 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Multipole moments continued: Relationship between spherical harmonic and Cartesian forms of multipole moments: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Consider previous example: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

General form of electrostatic potential in terms of multipole moments: 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Example of multipole expansion in evaluating energy of a very localized charge density r(r) in a electrostatic field F(r) (such as an nucleus in the field due to the electrons in an atom). 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Simple examples of multipole distributions y z x y z 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Another example of multipole distribution 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Another example of multipole distribution -- continued 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Another example of multipole distribution -- continued 02/02/2018 PHY 712 Spring 2018 -- Lecture 8

Another example of multipole distribution -- continued 02/02/2018 PHY 712 Spring 2018 -- Lecture 8