Module 3 : Nonlinear susceptibilities of materials
Lecture 18 : Organic Nonlinear Optical Materials
Instead of using the usual expansion of the first order wave-function in terms of unperturbed wave functions we can solve the equation as an inhomogenous differential equation. The solution is arbitrary to the extent that a constant multiple of unperturbed wave function can be added. We fix this constant such that
(18.17)
This gives an advantage that eigen values to order (2n+1) can be obtained from wavefunction to order n. [ L.I. Schiff, Quantum Mechanics, I II edition,(McGraw Hill, New York, 1968) p. 296].
In the second order,
(18.18)
Since is known in terms of the first order wave functions, Eq (18.18) can be solved again as an inhomogenous differential equation. This yields energies upto 5th order in the imposed electric field. Then using the eq (18.11) we obtain closed form expressions for linear and third order polarizabilities:
(18.19)
and
(18.20)
where a0is the Bohr radius. These results reveal several interesting aspects.
is known in terms of the first order wave functions, Eq (18.18) can be solved again as an inhomogenous differential equation. This yields energies upto 5th order in the imposed electric field. Then using the eq (18.11) we obtain closed form expressions for linear and third order polarizabilities: 
