Analyze limiting behavior for the general expression.
References are to equation numbers in: S.Mukamel, Principles of Nonlinear Spectroscopy (Oxford, 1995).
h is defined as h/2
(1)
(2)
Overdamped Oscillator
(3)
define
(4)
(5)
Overdamped Oscillator
for
(6)
Un
damped Oscillator
(7)
Under
damped Oscillator
(8)
Critically
(9)
(10)
h is defined as h/2
(11)
(12)
I
n the high temperature limit
(13)
Overdamped Oscillator
from (13)
(14)
This is Mukamel's eq. 8.71b
Un
damped Oscillator
from (10) - not high temp limit - Mukamel's eq. 8.68
(15)
from (13)
(16)
Under
damped Oscillator
From (12) - not high T
(17)
From (13)
(18)
Start with (13)
(19)
(this is Mukamel's eq. 8.69)