how to get the required list

Questions
1

I have the two variables L,m such that
L=0 => m=0
L=1 =>m=-1,0,1
L=2 =>m = -2,-1,0,1,2
(for each value of L, m is from -L to +L with increment 1)
now I want to generate a list with the order like
list= {{0,0},{1,0},{2,0},{1,-1},{2,-1},{1,1},{2,1},{2,-2},{2,2}}//
//all values of L for m=0
    all values of L for m=-1
    all values of L for m=1
    all values of L for m=-2
    all values of L for m=2
What should be the code for this list? kindly help and sorry for mistake in the text

2

Hi Adil,
Happy QM work!

In[70]:= (* create the list *)
nestedList = Table[{l, m}, {l, 0, 2}, {m, -l, l}];

In[71]:= (* flatten to individual states *)
lMlist = Flatten[nestedList, 1];

In[72]:= (* gather by the m state *)
gatherdByM = GatherBy[lMlist, #[[2]] &]

Out[72]= {{{0, 0}, {1, 0}, {2, 0}}, {{1, -1}, {2, -1}}, {{1, 1}, {2, 
   1}}, {{2, -2}}, {{2, 2}}}
3

Thanks David !! it really works :slight_smile:

4

Just an alternative:

m[l_] := Range[-l, l]

You can produce list:

res = Join @@ Function[x, {x, #} & /@ m[x]] /@ Range[0, 2]

This yields:

{{0, 0}, {1, -1}, {1, 0}, {1, 1}, {2, -2}, {2, -1}, {2, 0}, {2, 
1}, {2, 2}}

Gathering:

GatherBy[res, Last]

yields:

{{{0, 0}, {1, 0}, {2, 0}}, {{1, -1}, {2, -1}}, {{1, 1}, {2, 1}}, {{2, -2}}, {{2, 2}}}