Home >Documents >Funky Mathematical Physics Concepts Physics Concepts The Anti-Textbook* A Work In Progress. See...

Funky Mathematical Physics Concepts Physics Concepts The Anti-Textbook* A Work In Progress. See...

Date post:04-Feb-2020
Category:
View:1 times
Transcript:
• Funky Mathematical

Physics Concepts

The Anti-Textbook*

A Work In Progress. See elmichelsen.physics.ucsd.edu/ for the latest versions of the Funky Series.

Eric L. Michelsen

Tijxv x

Tijyv y

Tijzv z

+ dR

real

imaginary

CI

CR

i

-i

R

CI

“I study mathematics to learn how to think.

I study physics to have something to think about.”

“Perhaps the greatest irony of all is not that the square root of two is

irrational, but that Pythagoras himself was irrational.”

* Physical, conceptual, geometric, and pictorial physics that didn’t fit in your textbook.

https://elmichelsen.physics.ucsd.edu/ https://elmichelsen.physics.ucsd.edu/FunkyMathPhysics.pdf https://elmichelsen.physics.ucsd.edu/

• elmichelsen.physics.ucsd.edu/ Funky Mathematical Physics Concepts emichels at physics.ucsd.edu

2006 values from NIST. For more physical constants, see http://physics.nist.gov/cuu/Constants/ .

Speed of light in vacuum c = 299 792 458 m s–1 (exact)

Boltzmann constant k = 1.380 6504(24) x 10–23 J K–1

Stefan-Boltzmann constant σ = 5.670 400(40) x 10–8 W m–2 K–4

Relative standard uncertainty ±7.0 x 10–6

Avogadro constant NA, L = 6.022 141 79(30) x 1023 mol–1

Relative standard uncertainty ±5.0 x 10–8

Molar gas constant R = 8.314 472(15) J mol-1 K-1

Electron mass me = 9.109 382 15(45) x 10–31 kg

Proton mass mp = 1.672 621 637(83) x 10–27 kg

Proton/electron mass ratio mp/me = 1836.152 672 47(80)

Elementary charge e = 1.602 176 487(40) x 10–19 C

Electron g-factor ge = –2.002 319 304 3622(15)

Proton g-factor gp = 5.585 694 713(46)

Neutron g-factor gN = –3.826 085 45(90)

Muon mass mμ = 1.883 531 30(11) x 10–28 kg

Inverse fine structure constant  –1 = 137.035 999 679(94)

Planck constant h = 6.626 068 96(33) x 10–34 J s

Planck constant over 2π ħ = 1.054 571 628(53) x 10–34 J s

Bohr radius a0 = 0.529 177 208 59(36) x 10–10 m

Bohr magneton μB = 927.400 915(23) x 10–26 J T–1

Reviews

“... most excellent tensor paper.... I feel I have come to a deep and abiding understanding of relativistic

tensors.... The best explanation of tensors seen anywhere!” -- physics graduate student

https://elmichelsen.physics.ucsd.edu/ http://physics.nist.gov/cuu/Constants/

• elmichelsen.physics.ucsd.edu/ Funky Mathematical Physics Concepts emichels at physics.ucsd.edu

Contents

1 Introduction ........................................................................................................................................... 9 Mathematical Physics, or Physical Mathematics? ............................................................................ 9 Why Physicists and Mathematicians Argue ..................................................................................... 9 Why Funky? ..................................................................................................................................... 9 How to Use This Document ............................................................................................................. 9 Thank You .......................................................................................................................................10 Scope ...............................................................................................................................................10 Notation ...........................................................................................................................................10

2 Random Short Topics ..........................................................................................................................13 I Always Lie ....................................................................................................................................13 What’s Hyperbolic About Hyperbolic Sine? ...................................................................................13 Basic Calculus You May Not Know ...............................................................................................15 The Product Rule.............................................................................................................................16 Integration By Pictures ....................................................................................................................16 Theoretical Importance of IBP ........................................................................................................20 Delta Function Surprise: Coordinates Matter ..................................................................................20 Spherical Harmonics Are Not Harmonics .......................................................................................22 The Binomial Theorem for Negative and Fractional Exponents .....................................................23 When Does a Divergent Series Converge? .....................................................................................24 Algebra Family Tree .......................................................................................................................25 Convoluted Thinking ......................................................................................................................26 Two Dimensional Convolution: Impulsive Behavior ......................................................................27 Structure Functions .........................................................................................................................28 Correlation Functions ......................................................................................................................29

3 Vectors ...................................................................................................................................................30 Small Changes to Vectors ...............................................................................................................30 Why (r, θ, ) Are Not the Components of a Vector ........................................................................30 Laplacian’s Place ............................................................................................................................31 Vector Dot Grad Vector ..................................................................................................................39

4 Green Functions ...................................................................................................................................41 The Big Idea ....................................................................................................................................41 Boundary Conditions on Green Functions ......................................................................................46 Introduction to Boundary Conditions ..............................................................................................46 One Dimensional Boundary Conditions ..........................................................................................47 2D?? and 3D Green Functions ........................................................................................................53 Green Functions Don’t Separate .....................................................................................................53 Green Units .....................................................................................................................................54 Special Case: Laplacian Operator with 3D Boundary Conditions ..................................................55 Desultory Green Topics ..................................................................................................................58 Fourier Series Method for Green Functions ....................................................................................58 Green-Like Methods: The Born Approximation .............................................................................61

5 Complex Analytic Functions ...............................................................................................................63 Residues ..........................................................................................................................................64 Contour Integrals .............................................................................................................................65 Evaluating Integrals ........................................................................................................................65 Choosing the Right Path: Which Contour? .....................................................................................68 Evaluating Infinite Sums .................................................................................................................73 Multi-valued Functions ............................................................

Embed Size (px)
Recommended

Documents

Documents

Documents

Documents

Documents

Documents