py203_formulas.pdf - Formulas and Numerical Constants where...

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Formulas and Numerical Constants Lorentz transformation: The system S’ is moving with velocity ( v x , v y , v z ) = ( v, 0 , 0) relative to the S system. The Lorentz transformations are x = γ ( x vt ) , y = y, z = z, (1) t = γ t v c 2 x , (2) where γ = 1 / (1 β 2 ) 1 / 2 and β = v/c . The inverse Lorentz transformation corresponds to v → − v . Relativistic kinematics: In the following m always refers to the rest mass of a particle E 2 = p 2 c 2 + m 2 c 4 , (3) E = γ mc 2 p = γ mv, (4) and γ = (1 v 2 /c 2 ) 1 / 2 . The four vector ( E, pc ) transforms under Lorentz transformations like the four vector ( ct, x ): p x = γ p x vE/c 2 , p y = p y , p z = p z , (5) E = γ ( E vp x ) , (6) Black Body Radiation: Planck’s law is R ( λ ) = 2 π hc 2 λ 5 1 e hc λ k B T 1 . (7) The maximum of the distribution occurs at λ T = 2 . 898 · 10 3 K m. The total emissivity is given by the Stefan-Boltzmann law R = σ T 4 , σ = π 2 k 4 B 60¯ h 3 c 2 = 5 . 67 × 10 8 kg / s 3 / K 4 (8) De Broglie relations: De Broglie postulated the following relations between ( E, p ) and ( λ , f ) E = hf, ( E = ¯ h ω ) (9) p = h/ λ
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  • Fall '08
  • Reynolds,S
  • Fundamental physics concepts, wave function, Bohr radius, Lorentz Transformation, numerical constants

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