Selection Rules: Selection Rules Each of the spectroscopies have - - PowerPoint PPT Presentation

▶
selection rules selection rules
SMART_READER_LITE
LIVE PREVIEW

Selection Rules: Selection Rules Each of the spectroscopies have - - PowerPoint PPT Presentation

Feb 08, 2023 280 likes •424 views

Selection Rules: Selection Rules Each of the spectroscopies have associated selection rules. Selection rules originate from the quantum mechanical description of electromagnetic radiation interaction with matter. Use time-dependent

slide-1
SLIDE 1

Selection Rules:

slide-2
SLIDE 2

Selection Rules

CEM 484 Molecular Spectroscopy

Each of the spectroscopies have associated selection rules.

Selection rules originate from the quantum mechanical description

  • f electromagnetic radiation

interaction with matter.

Use time-dependent perturbation theory to derive probability of excitation between two states.

Consider a two-level system

2

slide-3
SLIDE 3

General Properties

CEM 484 Molecular Spectroscopy

Wavefunctions are

Normalized

Orthonormal

Wavefunctions are eigenstates of a specific operator

3

slide-4
SLIDE 4

Iclicker: Eigenstates

Which of the following functions are eigenstates of the hamiltonian, Ĥo = d/dx

A - Ψ = x

B - Ψ = x2

C - Ψ = ex

D - Ψ = ex^2

Molecular Spectroscopy CEM 484 4

slide-5
SLIDE 5

Perturbative Hamiltonian

CEM 484 Molecular Spectroscopy

Apply perturbation theory

H = Ho + H1

Ĥo is independent of time.

Separated time and spatial parts

ψ1(r,t) = ψ1(r) ψ1(t)

Ĥo ψ1 = E1 ψ1 = ihbar dψ1 /dt

Interaction with radiation is represented by perturbative component

Ĥ1 depends on time and radiation.

Ĥ1 = -mE = -mE0cos2pnt

5

slide-6
SLIDE 6

Total wavefunction

CEM 484 Molecular Spectroscopy

Total wavefunction a linear combination of eigenstates

ψ = (a1ψ1 + a2ψ2 )

Probability of finding system in state 2 at time t is given by

P1→2 = a2

*(t)a2(t) 

Finally get to P1→2 = |<m>12|d(E2-E1-hn)

6

slide-7
SLIDE 7

Excitation Probability (1)

CEM 484 Molecular Spectroscopy

Evaluate time-dependent Schrodinger equation to determine excitation probability

7

slide-8
SLIDE 8

Excitation Probability (2)

CEM 484 Molecular Spectroscopy

Evaluate time-dependent Schrodinger equation to determine excitation probability

8

slide-9
SLIDE 9

Excitation Probability (3)

CEM 484 Molecular Spectroscopy

Evaluate time-dependent Schrodinger equation to determine excitation probability

9

slide-10
SLIDE 10

Rotational Selection Rules (1)

CEM 484 Molecular Spectroscopy

Selection rule comes from

<m>12 = ∫ ψ2

* mz ψ1 dr

10

slide-11
SLIDE 11

Rotational Selection Rules (2)

CEM 484 Molecular Spectroscopy

Selection rule comes from

Summary

11

slide-12
SLIDE 12

Harmonic Oscillator Selection Rules (1)

CEM 484 Molecular Spectroscopy

Selection rule comes from

<m>12 = ∫ ψ2

* mz ψ1 dr 

mz(x) = m0 + (dm/dx)0q + …

12

slide-13
SLIDE 13

Harmonic Oscillator Selection Rules (2)

CEM 484 Molecular Spectroscopy

Selection rule comes from

<m>12 = ∫ ψ2

* mz ψ1 dr 

mz(x) = m0 + (dm/dx)0q + …

13

Summary