SLIDE 1
Hydrogen Energy Levels
- 20
- 10
10 20
- 14
- 12
- 10
- 8
- 6
- 4
- 2
hydrogen wavefunctions
5 10 15 20
- 14
- 12
- 10
- 8
- 6
- 4
- 2
Hydrogen Energy Levels -20 -10 10 20 -2 -4 -6 -8 -10 -12 - - PowerPoint PPT Presentation
Hydrogen Energy Levels -20 -10 10 20 -2 -4 -6 -8 -10 -12 - - PowerPoint PPT Presentation
Hydrogen Energy Levels -20 -10 10 20 -2 -4 -6 -8 -10 -12 -14 hydrogen wavefunctions 5 10 15 20 -2 -4 -6 -8 -10 -12 -14 n=3 1 0.5 5 10 15 20 25 30 -0.5 -1 -1.5 -2 -2.5 -3 100 200 210 211 300 310 311 320
SLIDE 2
SLIDE 3
n=3
5 10 15 20 25 30
- 3
- 2.5
- 2
- 1.5
- 1
- 0.5
0.5 1
SLIDE 4
100
SLIDE 5
200
SLIDE 6
210
SLIDE 7
211
SLIDE 8
300
SLIDE 9
310
SLIDE 10
311
SLIDE 11
320
SLIDE 12
321
SLIDE 13
322
SLIDE 14
Lyman forest α
SLIDE 15
Angular Momentum
- L =
r × p Lx = ypz − zpy, Ly = zpx − xpz, Lz = xpy − ypx px →
i ∂ ∂x
py →
i ∂ ∂y
pz →
i ∂ ∂z
[Lx, Ly] = [ypz − zpy, zpx − xpz] = [ypz, zpx] − [ypz, xpz] − [zpy, zpx] + [zpy, xpz] = ypx [pz, z] + pyx [z, pz] = i (xpy − ypx) = i Lz [Ly, Lz] = i Lx, [Lz, Lx] = i Ly
SLIDE 16
Angular Momentum
- L ·
L = L2 = L2
x + L2 y + L2 z
- L2, Lx
- =
- L2
x, Lx
- +
- L2
y, Lx
- +
- L2
z, Lx
- =
Ly [Ly, Lx] + [Ly, Lx] Ly +Lz [Lz, Lx] + [Lz, Lx] Lz = Ly (−iLz) + (−iLz) Ly +Lz (iLy) + (iLy) Lz =
- L2, Ly
- = 0,
- L2, Lz
- = 0
- L2,
L
- = 0
[AB, C] = ABC − CAB = ABC − ACB + ACB − CAB = A[B, C] + [A, C]B