Separation of Motion QM. Separation Vibration Rotation.

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Presentation transcript:

Separation of Motion QM

Separation Vibration Rotation

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) Square of the transition moment  n  e  m  2 2.Frequency of the light  3.Population difference (N m - N n ) 4.Resonance factor - Dirac delta function  (0) = 1

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) 1 Fermi’s Golden Rule Dipole Moment Matrix Elements

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) 1 Fermi’s Golden Rule

μ = q.r + - r Dipole Moments

CO 2 Vibrations

Einstein Coefficients nn mm

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) Square of the transition moment  n  e  m  2 2.Frequency of the light  3.Population difference (N m - N n ) 4.Resonance factor - Dirac delta function  (0) = 1

Frequency ●-----●

Problem 3 Devise a simple experiment using fairly everyday things to estimate the frequency of a light source …or alternatively devise an experiment to determine the wavelength and assume c = 30000kms -1

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) Square of the transition moment  n  e  m  2 2.Frequency of the light  3.Population difference (N m - N n ) 4.Resonance factor - Dirac delta function  (0) = 1

pedia.org/wi ki/Boltzmann _constant Boltzmann

nn mm oo N m = N o e -∆E/kT where ∆E = E m – E o

nn mm oo N m = N o e -∆E/kT where ∆E = E m – E o

Maser

 = (4  /3ħc)  n  e  m  2  (N m -N n )  (  o -  ) Square of the transition moment  n  e  m  2 2.Frequency of the light  3.Population difference (N m - N n ) 4.Resonance factor - Dirac delta function  (0) = 1

Dirac delta function δ (0) 1. Infinitely high 2. Infinitely narrow 3. Area = unity

Resonance commons.wikimedia.org

Millennium Bridge

Tacoma

ABC Rotation of a Diatomic Molecule