[Pw_forum] pdos

[Ari P Seitsonen]

Dear Ashkan Shekaari,

   Please check the documentation, for example in 
<QE_ROOT>/PP/Doc/INPUT_PROJWFC.def:

   text {
       Order of m-components for each l in the output:
         1, cos(phi), sin(phi), cos(2*phi), sin(2*phi), .., cos(l*phi), sin(l*phi)
       where phi is the polar angle:x=r cos(theta)cos(phi), y=r cos(theta)sin(phi)
       This is determined in file flib/ylmr2.f90 that calculates spherical harmonics.

       for l=1:
         1 pz     (m=0)
         2 px     (real combination of m=+/-1 with cosine)
         3 py     (real combination of m=+/-1 with sine)

       for l=2:
         1 dz2    (m=0)
         2 dzx    (real combination of m=+/-1 with cosine)
         3 dzy    (real combination of m=+/-1 with sine)
         4 dx2-y2 (real combination of m=+/-2 with cosine)
         5 dxy    (real combination of m=+/-2 with sine)
     }

     Greetings from Paris,

        apsi

-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-
   Ari Paavo Seitsonen / Ari.P.Seitsonen at iki.fi / http://www.iki.fi/~apsi/
     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935


On Sun, 8 May 2016, ashkan shekaari wrote:

> Dear experts,
> in quantum mechanics, the quantum number m is between -l and l : -l<=m<=l
> 
> and so m=-1, 0, +1 for l=1. but in the output of a pdos calculation, values of m 
> 
> are seen as follows:
> 
>      state #   9: atom   1 (Mo ), wfc  5 (l=2 m= 1)
>      state #  10: atom   1 (Mo ), wfc  5 (l=2 m= 2)
>      state #  11: atom   1 (Mo ), wfc  5 (l=2 m= 3)
>      state #  12: atom   1 (Mo ), wfc  5 (l=2 m= 4)
>      state #  13: atom   1 (Mo ), wfc  5 (l=2 m= 5)
> 
> Is, for example,  (l=2 , m= 1) equivalent to m=-2 or 
> 
>      (l=2 m= 1)------>  m=-2
>      (l=2 m= 2)------>  m=-1
>       (l=2 m= 3)------>  m=0
>       (l=2 m= 4)------>  m=1
>       (l=2 m= 5)------>  m=2
> 
> ?
> 
> --
> All the best,
> Ashkan Shekaari
> Plasma Physics Research Center, Science and Research Branch, 
> I A U, 14778-93855 Tehran, Iran.
> 
> On Sun, May 8, 2016 at 12:06 AM, ashkan shekaari <shekaari at gmail.com> wrote:
>       Dear experts,
> in quantum mechanics, the quantum number m is between -l and l : -l<=m<=l
> 
> and so m=-1, 0, +1. but in the output of a pdos calculation, values of m 
> 
> are seen as follows:
> 
>      state #   9: atom   1 (Mo ), wfc  5 (l=2 m= 1)
>      state #  10: atom   1 (Mo ), wfc  5 (l=2 m= 2)
>      state #  11: atom   1 (Mo ), wfc  5 (l=2 m= 3)
>      state #  12: atom   1 (Mo ), wfc  5 (l=2 m= 4)
>      state #  13: atom   1 (Mo ), wfc  5 (l=2 m= 5)
> 
> Is, for example,  (l=2 , m= 1) equivalent to m=-2 or 
> 
>      (l=2 m= 1)------>  m=-2
>      (l=2 m= 2)------>  m=-1
>       (l=2 m= 3)------>  m=0
>       (l=2 m= 4)------>  m=1
>       (l=2 m= 5)------>  m=2
> 
> ?
> 
> --
> All the best,
> Ashkan Shekaari
> Plasma Physics Research Center, Science and Research Branch, 
> I A U, 14778-93855 Tehran, Iran.
> 
> 
> 
>