Chemistry 475 -- Quantum Chemistry& Spectroscopy

Summary for Week 4&5

Monday, February 2 to Friday, February 13, 2009

Reading in Levine: Chapter 17.12 to 17.16

See handouts on

Expectation values and the Harmonic Oscillator

Two-body problem

Rigid Rotor

Hermitian Operators

Homework problems

Hand in on Monday, February 9: 17.46, 17.47, 17.51, 17.54, 17.55, 17.56, 17.64

EXAM on Levine Chapter 17 deferred to Friday, February 13.

Key Concepts

particles in multi-dimensions: particle in 2-D and 3-D box

degeneracy of quantum states; quantum levels

two-particle problem: diatomic rotation and vibration

harmonic oscillator is a good model for molecular vibration

two particle rigid rotor

Hermitian operators and operator algebra

Key Equations

n_x

n_y

n_z

E / (h²/8ma²)

Degeneracy

1

1

1

3

1

1

1

2

6

1

2

1

6

3

2

1

1

6

1

2

2

9

2

2

1

9

3

2

1

2

9

3

1

1

11

1

3

1

11

3

1

1

3

11

2

2

2

12

1

n_x	n_y	n_z	E / (h²/8ma²)	Degeneracy
1	1	1	3	1

1	1	2	6
1	2	1	6	3
2	1	1	6

1	2	2	9
2	2	1	9	3
2	1	2	9

3	1	1	11
1	3	1	11	3
1	1	3	11

2	2	2	12	1

Summary for Week 4&5

Reading in Levine: Chapter 17.12 to 17.16

Homework problems

Key Concepts

Key Equations

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