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Short "Derivations" of Key Formula of Modern Physics

Short "Derivations" of Key Formula of Modern Physics. W. J. Wilson Department of Physics & Engineering University of Central Oklahoma Edmond, OK 73034 Email: wwilson@ucok.edu Web: http://www.physics.ucok.edu/wwilson /. Outline.

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Short "Derivations" of Key Formula of Modern Physics

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  1. Short "Derivations" of Key Formula of Modern Physics W. J. Wilson Department of Physics & Engineering University of Central Oklahoma Edmond, OK 73034 Email: wwilson@ucok.eduWeb: http://www.physics.ucok.edu/wwilson/

  2. Outline • World’s Shortest Derivation of the Lorentz Transformation of SR • “Derivation” of Bohr Quantization Condition, • “Derivation” of Maxwell-Boltzmann Distribution • “Derivation” of Fermi-Dirac Distribution

  3. World’s 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

  4. y’ y v v t x’ x x’ x In O Frame, x’ (Length measure by O’) is Lorentz contracted So, solving for x’

  5. 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’

  6. Solve this for t’ But Thus, the Lorentz Transformation: So

  7. “Derivation” of Bohr Quantization

  8. “Derivation” of Bohr Quantization

  9. “Derivation” of Boltzmann Factor

  10. For ideal gas Isothermal (Exponential) Atmosphere:

  11. But So But the probability of finding a particle should be proportional to the density, so …

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