midterm exam equations

# midterm exam equations - Midterm Exam CHEM 482 please print...

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Unformatted text preview: Midterm Exam CHEM 482 October 28, 2009 ______________________________ please print your name There are 100 total points on this exam, as indicated in problems 1-6. There are no problems on pages 1 and 2, just information that may be useful to you. - (,) 1D TDSE separation of variables 1D TISE superposition of eigenfunctions (, ) = ( ) - / () = () ( ) = 1 = 2 2 2 () 2 =- 2 2 2 (,) 2 + ( ) ( ) = ( ) where + ( )(, ) = ( ) ( ) 0, 0 ( ) = , < 0 > QM Particle in a 1D Box: = = 8 2 2 2 2 QM Harmonic Oscillator: 0 = 1/4 1 2 0 2 2 = 2 1/4 where = /2 = + 1 2 4 3 - - 2 /2 1 2 2 /2 2 = 3 = 9 3 4 1/4 1/4 (2 3 - 3 ) - (2 2 - 1) - 2 /2 2 /2 Integration using spherical coordinates: = 2 sin ; (2 ) all space: 0 , 0 , 0 2 2 ( ) = 2 - 2 2 ( ) = - = 0 2 2 2 Integrals: 2 ( ) = 2 + 2 ( ) = - = 0 - = 0 2 2 2 4 3 - = 0 2 1 +1 1 ! - 4 (2 ) 4 ( > 0) - (2 ) 8 2 2 2 2 - = 0 4 - = 0 1 2 1 4 3 8 3 6 (2 ) 3 5 - 4 (2 ) 4 2 - 2 2 2 -1 8 3 (2 ) 2 = (0) + Perturbation Theory: 2 1 (1) = 2 2 (0) (0) H-atom TISE and related information: -2 2 () = 4 - 2 2 + 2 1 = 2 32 2 2 2 - 4 + 2 2 1 + () = () = 2 [()]2 Momentum operators: = - = - 2 = -2 1 + 2 1 2 2 Fundamental Constants and Conversions h = 6.626x10 -34 -31 Js kg J e = 1.60x10 -1 -19 C -27 c = 3.00x10 m/s kg J mn = 1.675x10 1 J = 1 kg m s -27 8 k = R/NA = 1.38x10 kg 23 -23 J/K me = 9.10x10 mp = 1.673x10 NA = 6.02x10 /mole 1 N = 1 kg m s -2 1 eV = 1.60x10 -19 1 cm = 1.99x10 -23 2 -2 ...
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