Need to find the orbital transition frequency

[matts014]

i need to find the orbital transition frequency
given by
ω=ω_a-ω_b
a and b represent orbital states a is higher energy state and b is lower energy state

 

[Simon Bridge]

Welcome to PF;
What sort of orbit, and how do you mean "frequency"?
Do you mean atomic orbitals and the frequency of the photon given off in a transition between them?

 

[matts014]

ω is the atomic orbital frequency
consider an atom of gas, for laser emission (photons) to take place there has to be transition of electron from outer orbital to lower orbital has to take place. so let a and b represents these orbital and a be outer orbital. transition dipole moment is given by
℘=√((3πε_0 ℏc^3 Γ)/ω^3 )
i need to find ω
this is given in the book "Quantum optics" by Scully M.O., Zubairy M.S. page 152 last paragraph

 

[Simon Bridge]

℘=√((3πε_0 ℏc^3 Γ)/ω^3 )

$$\rho = \sqrt{ \frac{3\pi\epsilon_0\hbar c^3}{\omega^3} }$$What is a transition dipole moment? What does it tell you?
http://en.wikipedia.org/wiki/Transition_dipole_moment

ω is the atomic orbital frequency

Oh OK - in post #1 you said that ω was the difference between two frequencies.

It helps if you understand the terms you are using.
i.e. Why would an atomic orbital have a frequency?

Note: the book you are using tells you the answer - earlier on: round about where the authors define "atomic orbital" for you.

 

[matts014]

need to find atomic transition frequency

sir,
to start with my aim is to generate a MATLAB code for emission of laser from remote puff of air(a remote sample of air). for that i have the the hamiltonian of the three level system.in that equation there are bracket operation , rabi frequency etc... my piriority now is to calculate the rabi frequency for the above equation. the air which i have considered here is having higher concentration of Oxygen. in this case the electrons from 2p will get exited to 3p by multi photon ionisation(2-photons at 226-nm) laser emission takes place when it gets de-excited from 3p to 3s at 845-nm. this is the process occurring i have rad this in an article which came in ieee spectrum magazine and another one from pnas.
now to calculate rabi frequency
it is given by
Ω=℘E/ħ
in this equation
E is the vector electric field amplitude
℘ is the transition dipole moment and is given by
℘=√((3πε₀ ℏc³ Γ)/ω³ )
where
ω is the transition frequency,
Γ is the spontaneous decay rate,
ħ is the reduced Planck constant,
c is the velocity of light,
ω is the transition frequency,
ε₀ is the vacuum permittivity.
now i am trying to calculate this transition frequency same as that explained in http://en.wikipedia.org/wiki/Atomic_electron_transition.
the book which i referred (for deriving hamiltonian of three level system)to specifies that
ω=ω_a-ω_b
a represents 3p state and b represents 3s state.
i am new to quantum mechanics. the knowledge which i have is limited so any suggestions are welcome. please do suggest me reference books.
thankyou