Short "Derivations" of Key Formula of Modern Physics

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Short "Derivations" of Key Formula of Modern
Physics

• W. J. Wilson
• Department of Physics Engineering
• University of Central Oklahoma
• Edmond, OK 73034
• Email wwilson_at_ucok.eduWeb http//www.physics.
  ucok.edu/wwilson/

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Outline

• Worlds Shortest Derivation of the Lorentz
  Transformation of SR
• Derivation of Bohr Quantization Condition,
• Derivation of Maxwell-Boltzmann Distribution
• Derivation of Fermi-Dirac Distribution

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Worlds Shortest Derivation of the Lorentz
Transformation

• We assume that in the previous lecture one has
  developed the time dilation
• And the Lorentz contraction formulae in the usual
  way
• Where

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y
y
v
v t
x
x
x
x
In O Frame, x (Length measure by O) is Lorentz
contracted
So, solving for x
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y
y
v
v t
x
x
x
x
In O Frame, x is Lorentz contracted
But as we just showed
So
Solve this for t
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Solve this for t
But
Thus, the Lorentz Transformation
So
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Derivation of Bohr Quantization
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Derivation of Bohr Quantization
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Derivation of Boltzmann Factor
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For ideal gas
Isothermal (Exponential) Atmosphere
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But
So
But the probability of finding a particle should
be proportional to the density, so