exam1 - < x 2>= a 4 ⎢ ⎢ 4 3 n 2 2 ⎥ ⎥ a 2 ⎣...

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RG^2 and TV^2 1 st Hour Exam 10/04/07 USEFUL CONSTANTS and FORMULAS 1mW = 10 -3 W = 10 -3 J s -1 1nm = 10 -9 m 1eV = 1.602 x 10 -19 J h = 6.63 x 10 -34 J s ! = 1.05 x 10 -34 J s c = 3.0 x 10 8 m s -1 hc = 2.0 x 10 -25 J m m e = 9.11 x 10 -31 kg e = 1.602 x 10 -19 C 12 2 1 3 λν = c ε 0 = 8854 . × 10 Cs kg m E = h ν λ = h / p l n = mrv = n_ r n = n 2 a 0 a 0 = 5.29 x 10 -11 m 1 Z 2 me 4 1 me 4 E = = ( 2.18 x 10 18 J ) R = = 109,678 cm -1 n n 2 8 0 2 h 2 n 2 8 0 2 h 3 c E = k = ! 2 k 2 2 π ψ x A cos kx ( ) ( ) = ( ) + B sin kx 2 m n x E n = n 2 h 2 2 ( 0 x a ) = 2 sin a Δ x Δ p _ /2 8 ma a 2 , < x >= for Particle in Box of length “a”, for x=0 to x=a,
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Unformatted text preview: < x 2 >= a 4 ⎢ ⎢ 4 3 ( n 2 ) 2 ⎥ ⎥ a 2 ⎣ ⎦ x ˆ = x p ˆ = ! i dx d l ˆ z = ! i d d φ e ± i θ = cos ± i sin ∫ cos x dx = sin x ∫ sin x dx = − cos x ∫ sin 2 y dy = 2 1 y − 4 1 sin(2 y ) ∫ cos 2 y dy = 2 1 y + 4 1 cos(2 y ) ∞ ∞ ∫ 0 e − ax dx = a 1 [ a > 0] ∫ x n e − ax dx = a n n + ! 1 [ n positive integer , a > 0] 1 2 e 8...
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This note was uploaded on 11/27/2011 for the course CHEM 5.43 taught by Professor Timothyf.jamison during the Spring '07 term at MIT.

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