[Pw_forum] Definition of the projector function output in the "file_beta" file by LD1.

[Wei Chen (weic@Princeton.EDU)]

Dear Paolo:

I am wondering about the definition of the projector function output in the "file_beta" file produced by LD1. Is it defined as the TRUE beta function multiplied by r ? (Just like the AE and PS radial wavefunctions output in ld1.wfc and ld1ps.wfc are actually the TRUE radial wavefunctions multiplied by r. )

I guess this is the case, because the true projector function needs to satisfy  < projector_i | \phi^PS_j > = \delta_ij. 
where \phi^PS_j is the PS partial wave. 
I checked with the output of "file_beta" (\beta_i ), and ld1ps.wfc (\phi^PS_j), and I found the following is true:

\int  (\beta_i / r )  *  (\phi^PS_i  / r )  *  r^2 dr = 1                          

Am I right about the output in the "file_beta" file? 
Thank you very much for your kind clarification and help!

Wei Chen
Email: weic at princeton.edu
Princeton University