formation of lowering operator and raising operator
- To: mathgroup at smc.vnet.net
- Subject: [mg118986] formation of lowering operator and raising operator
- From: tarun dutta <tarunduttaz at gmail.com>
- Date: Thu, 19 May 2011 07:40:24 -0400 (EDT)
i have a basis like" ket={0,1,2,3}"
define lowering operator as "Ai "where i can vary from 0 to 4
I need to operate it on the ''ket' such as
A3{0,1,2,3} will give the result as Sqrt[2]{0,1,1,3} ,here i=3;
similarly, A2{0,1,2,3} will give result as Sqrt[1]{0,0,2,3} here i=2
In general Ai{0,1,2,....i,,,,3,,,}===sqrt[i]{0,1,2,...i-1,...3...}
one constraint if A0{0,1,2,3} will give==Sqrt[0]{0,1,2,3}
since number can not be negative within the basis..
In the same way if raising operator Bi operate on {0,1,2,3}
as Bi{0,1,...i....,2,3} will give sqrt[ i+1]{0,1,2.....i+1,...2,3}
how will i construct it in mathematica?
any help will be much appreciated..
regards,
tarun dutta