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CHEM 313 (1)

data_sheet.pdf

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Department
Chemistry
Course
CHEM 313
Professor
Nicholas Mosey
Semester
Fall

Description
Data Sheet 1. Physical Constants. Page 1 of 6 2. More physical constants. kB= 1.3806503 × 10 -23m kg s K2 -1 -27 1 amu = 1.66053886 × 10 kg 1 Å = 1.0 × 10 -10m  = 3.14159 3. Basic quantum theory (and related). h h 2 E  h    c    A A  A p mv 2 ˆ ˆ ˆˆ ˆˆ  ˆ ˆ 1 2 *ˆ  A,B  A BA   A b  A,B   2 A  Ad   ˆ A  a 4. Operators. ˆ p 2 2 2 2  2 2 2  d ˆ ˆ ˆ T        2 2 2 p x i H T V x  x 2m 2m 2m  y z  dx 5. Particle in a 1D box with infinite walls.  if x 0 2  2 2  nx  n 2 2 V   0 if 0 x  L H   2  n sin  E n 2 2m x L  L  2mL  if x  L 6. 1D harmonic oscillator. 2 d 2 1 2  1  1 2 x 2 H   2  kx En  n   n N H n n   2 dx 2  2  2 H 0  1 x 1 H 1x  2 x 1 2 H 2x  4 x 1 2  2 1 2 1 2 3 1 2 1 2 H n1 H 3   8    12 x  xH  n nH n1 2 Page 2 of 6 1 4  1 4x22 4 3  x22   1 4 2 x22  0   e  1   xe  2   2x  1 e       4  1 4  3  3 x 2 1 1  3   2x  3x e a  X iP ˆ a X iPˆ  9  2 2 ˆ   ˆ 1 2 d m1m 2 2 X  x  x Px   p x i  dx   m  m k   1 2   2   h   k   1 k   1 k 2  2c  7. Rigid Rotor. 2 2  H   1  sin     1  2I sin      sin   2    2  L   2 1   sin    1   sin     sin   2   1 2 m  m  2J 1 J  m !  m im  Y J ,    m  4 J  m !  P J os e      1 2 1 2 1 2 0 1 0  3  1  3  i 1  3  i Y0 Y 1 4  cos Y1  8  sin e Y1 8  sine 4       LY m 2J J 1Y m LY  mY m E  BJ J 1 J   J z J J J   h B  2 I  l2 8 cI 8. Hydrogen atom. 2 e2 H    e2  ,,  r Y  m ,  2m e 4 0 ˆ 2 1   2   1     1 2  e H    2 r  2 sin  2 2 2  2m e r r  r r sin      r sin    4 r0 Page 3 of 6     1 er 0   1 2  r  er 20   1 r er 20sin cos 1s 3 2s 3  a  2 x 3 a a 0 4 2a 0   0 4 2a 0 0 1 r r 20 1 r r 20  2 y 3 e sin sin  2zp 3 e cos 4 2a 0 a0 4 2a 0 a0   2 r0a 1  r  r 20 1 r r 20 R 10   3 e R20  3 1 e R21  3 e  a0  2a 0  2a 0 24a 0 a0 4 2 1  m e  E h 1 1 1  e  E n  2  2 2 2   2  R H 2   2   n 32  0  2 n n n 8 0 0  9. Variational Principle. * ˆ * ˆ  Hd   Hd k * * E  * E 0 *    ci i H ij  iˆ j S ij  i j   d
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