PHYS 7211

ADVANCED TOPICS IN MATHEMATICAL METHODS OF THEORETICAL PHYSICS;
MATHEMATICAL FOUNDATIONS IN QUANTUM MECHANICS.


(PREREQUISITE: PHYS 4112 OR EQUIVALENT)

FALL 2010

CLASS: 10:30AM–12:00N T-TH, Nicholson 118

Prof. Jonathan P. Dowling

Office Hours: 12:00N–1:00PM T-Th

Grader: Robert Beaird


REQUIRED BOOK:

Elements of Green's Functions and Propagation: Potentials, Diffusion, and Waves
by
Gabriel Barton
Oxford University Press (1989) and Reprinted (2005)
ISBN13: 9780198519980, ISBN10: 0198519982


RECOMMENDED BOOKS:

Mathematical Methods for Physicists, 5th Edition
by
George B. Arfken and Hans J. Weber
Academic Press (2001), ISBN: 0-12-059825-6
The PDFs for Arfken and Weber, 5th Edition, is online here but password protected.  The password was sent to you in an email.
ArfkenWeber05 is the entire book at low resolution.  ArfkenWeber05.4 is only Chapter 4, but at higher resolution.
Chapters 4, 6, and 7 are all we are covering in class, and are are all available at higher resolution following this notation.


Mathematics of Classical and Quantum Physics
by
Fredrick W. Byron, Jr. and Robert W. Fuller
Dover Publications (1992), ISBN: 048667164X
This book is very good and  more mathematically intensive, and also very cheap, only $14 online.


REQUIRED SOFTWARE:
Acrobat Reader 9.1 (PDF) & Mathematica 7.01 (NB)
Available in PAWS 
Tigerware!

NRL PLASMA FORMULARY
GRAD, DIV, CURL, AND ALL THAT!



COURSE GRADE:
100% Homework

SYLLABUS


Arfken & Weber

Chapter 4:  Group Theory

Chapters 6.1–6.5 & 7.1–7.2, 7.4: Complex Analysis

Barton

Part I: Introduction
Chapter 01: The Dirac Delta Function
Chapter 02:  Ordinary Differential Equations
Chapter 03: Partial Differential Equations

Part II: Potentials
Chapter 04: Poisson's Equation I — Introduction
Chapter 05: Poisson's Equation II — Dirichlet Boundary Conditions
Chapter 06: Poisson's Equation III — Neumann Boundary Conditions

Chapter 07: Poisson's Equation IV — Points of Principle

Part III: Diffusion
Chapter 08: The Diffusion Equation I — Unbounded Space
Chapter 09: The Diffusion Equation II — General Theory and Schrödinger's Equation

Part IV: Waves
Chapter 10: The Wave Equation I — General Theory
Chapter 11: The Wave Equation II — Unbounded Space
Chapter 12: The Wave Equation III — Retarded and Advanced Solutions, Radiating Sources, Boundaries and Reflections

Part V: The Helmholtz Equation
Chapter 13: Kirchoff Wave-Diffraction Theory


HOMEWORK         ASSIGNED         DUE                 HINTS                        SOLUTIONS
HW01                   THU 26 AUG      THU 02 SEP                                                          HW01SOL
HW02                   THU 02 SEP       THU 09 SEP           HW02HINTS                         HW02SOL
HW03                   THU 09 SEP       THU 16 SEP           HW03HINTS                         HW03SOL
HW04                   THU 16 SEP       THU 23 SEP          PROB1.9 typo                         HW04SOL
HW05                   THU 23 SEP       THU 30 SEP           HW05HINTS                         HW05SOL
HW06                   THU 30 SEP       THU 07 OCT                                                          HW06SOL               
HW07                   THU 07 OCT      THU 14 OCT                                                          HW07SOL
HW08                   THU 14 OCT      THU 28 OCT                                                         HW08SOL
HW09                   THU 28 OCT      THU 04 NOV                                                         HW09SOL
HW10                   THU 04 NOV     THU 11 NOV                                                          HW10SOL
HW11                   THU 11 NOV     THU 19 NOV                                                         HW11SOL
HW12                   THU 25 NOV     THU 08 DEC                                                                                                                           

LECTURES                                                                                                                         

ARFKEN & WEBER
LECT01TUE24AUG10
LECT02THU26AUG10
LECT03TUE31AUG10
LECT04THU02SEP10

BARTON
CH1.1-1.3
CH1.4

CH2.1-2.2      SEC.2.2.13.NB   SEC.2.2.13.NB.PDF
CH2.3
CH2.4

CH3.1-3
CH3.4-5

CH4.1-3
CH4.4-5

CH5.1.1-5.3.2
CH5.3.3-5.5

CH6.0-6.3
CH6.4

CH8.1-8.3
CH8.4

CH10.1-10.3.2
CH10.3.3-10.4.1
CH10.5.1-2.PDF         CH10.5.1-2.NB
CH10.5.3
CH10.5.3.X


SPECIAL EVENTS
TUE 24 AUG:   FIRST DAY OF CLASS
THU 21 OCT:   FALL HOLIDAY
THU 25 NOV:  THANKSGIVING HOLIDAY
THU 02 DEC:   LAST DAY OF CLASS
THU 08 DEC:   LAST HW12 DUE