V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are...

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Transcript of V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are...

Page 1: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

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Page 2: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

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Page 3: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

The wavefunctions of the Simple Harmonic Oscillator are

Orthonormal

Page 4: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

Orthonormal wavefunctions

Page 5: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

∫+ ∞

- ∞ψv” ψv’ dτ = δv” v’

Orthonormal wavefunctions

Page 6: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

∫+ ∞

- ∞ψv” ψv’ dτ = δv” v’

Orthonormal wavefunctions

Kronecker delta δij = 1 when i = j and 0 when i ≠ j

Page 7: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

+ +

∫+ ∞

- ∞ψv=0 ψv =0 dτ = 0

Orthonormal wavefunctions

← – ∞ + ∞ →

Page 8: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

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Page 9: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

+–

∫+ ∞

- ∞ψv=1 ψv =0 dτ = 0

Orthonormal wavefunctions

← – ∞ + ∞ →

Page 10: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

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Page 11: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

+ +–

∫+ ∞

- ∞ψv=2 ψv =0 dτ = 0

Orthogonal wavefunctions

← – ∞ + ∞ →

Page 12: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

Anharmonic oscillator wavefunctions and probabilities

Page 13: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

Anharmonic oscillator wavefunctions and probabilities

Page 14: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

Anharmonic oscillator wavefunctions and probabilities

Page 15: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

Anharmonic oscillator wavefunctions and probabilities

Page 16: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

Anharmonic oscillator wavefunctions and probabilities

Page 17: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 18: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 19: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

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Page 20: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 21: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

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0

y = x2

Page 22: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 23: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 24: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 25: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 26: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 27: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 28: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 29: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 30: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 31: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 32: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 33: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 34: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 35: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 36: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 37: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

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8

6

4

2

0

y = x2

Page 38: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 39: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 40: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

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y = x2

Page 41: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

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6

4

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0

y = x2

Page 42: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

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y = x2

Page 43: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

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8

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y = x2

Page 44: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

0

y = x2

Page 45: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

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y = x2

Page 46: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

x →

↑y

-8 -6 -4 -2 0 2 4 6 8

12

10

8

6

4

2

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y = x2

Page 47: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

http://en.wikipedia.org/wiki/File:Simple_harmonic_oscillator.gif

Page 48: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

H + H

E(r)

r

0

Rotational levels

Continuum wavefunction of a dissociating state

Page 49: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

http://131.104.156.23/Lectures/CHEM_207/uv-vis.htm

Page 50: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 51: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html

Page 52: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 53: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 54: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 55: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 56: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 57: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

H + H

r

E(r)

H2

Page 58: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 59: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 60: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 61: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.
Page 62: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

http://jchemed.chem.wisc.edu/JCEDLib/SymMath/collection/article.php?id=29

Page 63: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.

http://www.pci.tu-bs.de/aggericke/PC3e_osv/Kap_III/Molekuelschwingungen.htm

Page 64: V6543210V6543210. V6543210V6543210 The wavefunctions of the Simple Harmonic Oscillator are Orthonormal.