FinalExamEqnSheetsME501F2007

# FinalExamEqnSheetsME501F2007 - 1 Equation Sheets TdS...

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1 Equation Sheets TdS Equations: du T ds Pd h u P g h T s f u T s vv ,,, [] [ ( l n) ] dg RT d f TT ds Q T rev / First Law - Closed System: UQW neglecting KE, PE First Law - Open System: neglecting KE, PE  v shaft CV CS d QW u d u P V d A dt     Specific Heats: ; PV PP hs u s cT c T T T      Schrödinger wave equation: 2 2 (,) (,) (,) 2 rt ir t V r t r t tm    Time-independent Schrödinger wave equation: 2 2 () () () 2 rV r r r m   Normalization Condition: * 1( , ) ( , ) r t r t d three- dimensional form   Dynamical Variable Operator r op rr p op p i   , xop pi x pp p 2 p op 22 2   op i t B r p (, ) B B r i op (, ) ˆˆ ˆ 11 ˆ sin r x y z Cartesian coord xyz e e e spherical coord r   

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2 222 2 2 22 2 2 2 11 1 sin sin sin Cartesian coord xyz r Spherical coord rr r r r         Expectation Values: * (,) op B r t B r t d three dimensional form     2 , sin d dx dy dz Cartesian coord d r dr d d Spherical coord   * op B x t B x t dx one- dimensional form     2* op op B x t B B x t dx one dimensional form   Molecular Energy Levels 2 (v) v v vib ee e Gx hc   with zero-point energy included 2 v v v vib e hc zero-point energy subtracted, G(0) = 0 vv v () ( 1 ) ) rot FJ BJJ DJ J hc v 1 v 2 BB  3 v 2 4 v e e e B D D for all Degeneracies: 2 1 1 rot vib gJ g  Rigid Rotator, Harmonic Oscillator e e 1 ) ) ( v ) v 2 rot rot vib rot B JJ G hc k hc  
3 Characteristic Temperatures: ee 1 1.439 rot vib BB B hc K B kk k c m   Term Symbols Atomic: 2S+1 L J , J = (L+S), (L+S-1), .

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FinalExamEqnSheetsME501F2007 - 1 Equation Sheets TdS...

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