PDF file with an explanation of FT theory one can find here.

SCHEME N1 (the best):

Direct FT:

Practical implementation if FT routine is based on standart Numerical Receipes (NR) routine which simply solves the system of equations (2) (see PDF file) with known boundary conditions G'(0) and G'(n) i.e. one has to know the first derivatives at the boundaries.

To find those derivatives one has to use Eq.(16) .

The practical implementation of FT is based on two routines

  1. nfourier1 (NR routine to solve the system of Eq.(2)
  2. FDeS (the first derivatives calculation, general case) or FDeSSUN (in the of SU(N) case)

Inverse FT:

The inverse FT is also describes in the PDF file and corresponding Fortran routine name is InvFourierNew.

SCHEME N2 (still quite good):

Another way to make FT in QMC program is via moments. IT is given via solution of the system of Eqs.(3) with the moments Eqs.(11)-(13) (or Eqs.(14)-(15) in the SU(N) case).

The practical implementation of FT is also based on two routines:

  1. nfourier2
  2. moments (or moment in the SU(N) case).

SCHEME N3 (the worst):

The natural spline routines have names nfourier and invfourier for the direct and inverse FT correspondingly.


  1. If one does not knows much about the system but still wants to use something better then the natural spline. There is an 5-point interoilation formula (routine name is FDfit) to obtain the voundary derivatives and use scheme 1.
  2. All the mentioned routines one can find in Codes section

Last updated: June 23, 2003