Cheatsheet for Introduction to Modern Physics | PHYS 3141, Study notes of Physics

Download Cheatsheet for Introduction to Modern Physics | PHYS 3141 and more Study notes Physics in PDF only on Docsity! Lorentz Transformations Position Transforms )(' ' ' )(' 2c vxtt zz yy vtxx −= = = −= γ γ Inverse )''( ' ' )''( 2c vxtt zz yy vtxx += = = += γ γ Velocity Transforms ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ − = − = − −= 2 2 2 1 ' 1 ' 1 ' c vu u u c vu u u c vu vuu x z z x y y x x x γ γ Inverse ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + = + = + += 2 2 2 '1 ' '1 ' '1 ' c vu u u c vu u u c vu vuu x z z x y y x x x γ γ Doppler Effect c v c v ff o m1 1± = Time Dilation γτ=Δt Length Contraction γ pLL = Spacetime interval ][)( 22222 zyxtcS Δ+Δ+Δ−Δ=Δ Relativistic Energy 22 2222 2 )()( mcmckE E mcE mcpc −= = = + γ γ For a photon: E=pc Relativistic Momentum ump rr γ= Gamma 2 2 1 1 c v− =γ Newton’s second law )( )( icrelativistnonmaF generalin dt dpF −= = Centripetal acceleration r va 2 = Particle Decay Center of mass Kinematics Coulomb force and Potential r qkq U r qkq F 21 2 21 = = Blackbody Radiation 1)exp( 8)( 10898.2 /1067.5 5 3 428 4 − = ⋅×= = ×= = − − − Tk hc hcu Kmc cT KmW TR B o om λ λπλ λ σ σ