EqnSheetExam2ME501F2007

# EqnSheetExam2ME501F2007 - 1 Equation Sheets TdS Equations:...

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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 = δ / First Law - Closed System: Δ UQW = neglecting KE, PE First Law - Open System: neglecting KE, PE ± ± QW d dt ud uP Vd A shaft CV CS −= + + z z ρρ v a f G G Specific Heats: ; PV PP hs u s cT c T T T ∂∂ ⎛⎞ == = = ⎜⎟ ⎝⎠ Schrödinger wave equation: i rt tm Vrt = G = G G G ∂Ψ =− + (,) (,) (,) 2 2 2 ΨΨ Time-independent Schrödinger wave equation: −∇ + = = G G G G 2 2 2 m rV r r r ψψ ε ψ () () () Normalization Condition : 1 =∀ zzz * G G rt d th r ee fo rm dimensional Dynamical Variable Operator G r G G r r op = G p G = p i op = − pi x xop , = G G G pp p 2 = G = p op 22 2 = − ε op i t = = B r p (, ) GG B B r i op = (, ) G =

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2 Equation Sheet #2 ∇= + + + + F H G I K J + F H G I K J + ±± ± sin sin sin x x y y z z Cartesian coord xyz Cartesian coord rr r r Spherical coord ψ ∂ψ ∂θ θ ∂φ 2 2 2 2 2 2 2 2 2 2 22 2 2 2 11 1 Expectation Values: Br t B r t d t h r e e f o r m op =∀ zzz ΨΨ * (,) G G dimensional d dx dy dz Cartesian coord d r dr d d Spherical coord ∀= , sin 2 θθ φ B x t B x t dx one form op =− −∞ +∞ z * dimensional B x t B B x t dx one form op op 2 −∞ +∞ z * ot dimensional Molecular Energy Levels ε ωω vib ee e hc Gx == + + F H G G I K J J F H G G I K J J () vv v 1 2 1 2 2
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## This note was uploaded on 12/26/2011 for the course ME 501 taught by Professor Na during the Fall '10 term at Purdue.

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EqnSheetExam2ME501F2007 - 1 Equation Sheets TdS Equations:...

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