# [Pw_forum] pdos

Ari P Seitsonen Ari.P.Seitsonen at iki.fi
Sat May 7 21:56:14 CEST 2016

```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.
>
>
>
>
```

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