equation sheet

equation sheet - Chem 110A 1 Equations Particle in a 1D...

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Unformatted text preview: Chem 110A 1 Equations Particle in a 1D box: " n x ( ) = 2 L sin n # x L $ % & ( ) E n = n 2 " 2 h 2 2 mL 2 = n 2 h 2 8 mL 2 Harmonic Oscillator: H = " h 2 2 d 2 dx 2 + k 2 x 2 = m 1 m 2 m 1 + m 2 " x ( ) = # $ % & ( ) * 1/4 e + # x 2 /2 " 1 x ( ) = 4 # 3 $ % & ( ) * 1/4 xe + # x 2 /2 " 2 x ( ) = # 4 $ % & ( ) * 1/4 2 # x 2 + 1 ( ) e + # x 2 /2 " 3 x ( ) = # 3 9 $ % & ( ) * 1/4 2 # x 3 + x ( ) e + # x 2 /2 with E n = n + 1 2 " # $ % & h ( ( = k ) = k h 2 " # $ % & 1/2 Operators 1D: p x = " i h # # x H = " h 2 2 m # 2 # x 2 + V x ( ) 3D: p =-i h " H = " h 2 2 m # 2 + V x , y , z ( ) 2 = 2 x 2 + 2 y 2 + 2 z 2 volume element: dxdydz = r 2 sin " drd " d # " 2 = 1 r 2 # # r r 2 # # r + 1 r 2 sin $ # #$ sin $ # #$ + 1 r 2 sin $ # 2 #% 2 Constants and Units E h = 27.211 eV = 4.3597 10 18 J atomic units: h = m e = a = e / 4 "# = 1 fine structure constant: " = h m e ca = 1 137.036 atomic unit of time = 24.18924....
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This note was uploaded on 12/02/2009 for the course CHE 110A taught by Professor Mccurdy during the Spring '09 term at UC Davis.

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equation sheet - Chem 110A 1 Equations Particle in a 1D...

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