       Efficient use of coefficient--Efficient simplification

```I wish to simplify expressions such as the following which possess terms
involving ket[n+i]. They involve a variable range of indices i.

Out=
-(Sqrt[n] (Sqrt[-1 + n] ket[-2 + n] - Sqrt[n] ket[n])) +

Sqrt[1 + n] (Sqrt[1 + n] ket[n] - Sqrt[2 + n] ket[2 + n])

I can collect the various terms in ket[n+i] with the following
operation:

In:=
Out//Expand// Table[ket[n+i] Coefficient[#,ket[n+i]  ],{i,-2,2}]&
//Plus @@ #&

Out=
-(Sqrt[-1 + n] Sqrt[n] ket[-2 + n]) + (1 + 2 n) ket[n] -

Sqrt[1 + n] Sqrt[2 + n] ket[2 + n]

My problem is this, Since I do no know what the range of ket[n+i] will
be, I would like to write a general expression that will find what
ket[n+i] are present and collect the coefficients of each of these. The
inelegant wat is to run over a range of i's that will surely bracket
any ket[n+i] that I will possibly encounter, but that is distasteful.
I am using version 2.2  but will probably switch to 3.0 soon.

Any other suggestions to that way I have done things are welcomed.  If
possible, please copy me on email since I might otherwise miss posts to
the newsgroup.

cannon@alpha.centenary.edu

Thanks very much,

------------------------------------------------------------------------------
Joel W. Cannon                 |   (318)869-5160          Dept. of
Physics               |   (318)869-5026  FAX    Centenary College of
Louisiana |       P. O. Box 41188		       |
Shreveport, LA 71134-1188      |

```

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