Subject: Role of the Fourier Transform in TDDFT

From: "Telkuni" <[email-masked]>
Date: Wed, 13 Mar 2002 21:28:46 +0900

Hello! CCLers,

 I'm learning TDDFT. I have one question which is the role of its Fourier
transform.  All responses, I will appreciate. And I will summarize the replies,
send it to CCL.

  I have read some papers:

  1 )M. Petersilka
　Excitation Energies from Time-Dpendent Density-Functional Theory
　Phys. Rev. Lett. 76, p1212 (1996)

  2) M E Casida
  Time-Dependent Density Functional Response Theory for Molecules
　-RECENT ADVANCES IN DENSITYFUNCTIONAL METHODS (Part I)

and so on...

  Although the Fourier transform was used on these papers, I can't find 
the reason(s) why we must do Fourier transform in TDDFT.

  On "Density-functional approach to local-field effects in finite systems: 
Photoabsorption in the rare gases"(by A.Zangwill and P.Soven, 
Phys. Rev. A, vol.21, pp1561 (1980)), there is a description:
  "The induced density and external potential are related through a position-
    and frequency-dependent complex susceptibility".
  Maybe, I think it is necessary to know the perturbation frequency by converting
the time-domain with Fourier transform ( time -> omega, to calculate the energy 
with the frequency).

  But I'm wondering, can we get perturbation frequency "only with" the Fourier 
transform? Because the transform has been originally used to divide or analyze 
complex wave(s).

  If someone knows the necessity and reason(s) of the Fourier transform 
in TDDFT, or knows the articles which describe the role of transform, please 
teach me.

   Best regards,
   Telkuni

-------------------------------------------------
   Telkuni Tsuru     [email-masked]