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Introduction to String Theory

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Strings in Curved Spacetime

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Introduction to Superconductors

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Supersymmetry (SUSY) and Grand Unified Theory (GUT)

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test

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The Standard Model

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Electroweak Unification (Glashow-Weinberg-Salam)

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Gauge Theories (Yang-Mills)

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Gravitational Force and the Planck Scale

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Introduction to the Standard Model

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Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

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Quantum Flavordynamics and Quantum Chromodynamics

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Special Unitary Groups and the Standard Model - Part 1

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Special Unitary Groups and the Standard Model - Part 2

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Special Unitary Groups and the Standard Model - Part 3

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Standard Model Lagrangian

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The Higgs Mechanism

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The Nature of the Weak Interaction

Topology

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Units, Constants and Useful Formulas

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Last modified: January 26, 2018



Compton Effect
--------------
Photons scattered from electrons had longer wavelength than those incident 
upon the target.  Gave clear and independent evidence of particle-like behavior 
in support of the photoelectric effect.

                recoiled electron p_e= √(E² - (m_ec²)²)/c
                    ^
                   /
                  /
                 /
 photon ------->o.....
 p_i = h/λ_i       \θ
                  \
                   \
                    v
               scattered photon
               p_f = h/λ_f

Conservation f energy:
hν_i + m_ec² = hν_f + √(p_e²c² + m_e²c⁴)

Conservation of momentum:
_    _    _
p_i = p_e + p_f
       _    _    _   _
p_e² = (p_i - p_f).(p_i - p_f)
    = p_i² + p_f² - 2p_ip_fcosθ

multiply by c² and substitute E = pc = hν

(p_ec)² = (hν_i)² + (hν_f)² - 2h²ν_iν_fcosθ

square energy conservation expression to get

(p_ec)² = (hν_i)² + (hν_f)² - 2h²ν_iν_f + 2m_ec²(hν_i - hν_f)

-2h²ν_iν_fcosθ = -2h²ν_iν_f + 2m_ec²(hν_i - hν_f)

which leads to 

λ_f - λ_i = (h/m_ec)(1 - cosθ)

Compton Wavelength
--------------------

The Compton wavelength of a particle is equivalent to the wavelength 
of a photon whose energy is the same as the rest-mass energy of the 
particle.

The Compton wavelength, λ, is derived as follows:

E = hf = hc/λ = mc²

∴ λ = h/mc