Groups > comp.soft-sys.math.mathematica > #2494

formation of lowering operator and raising operator

From	tarun dutta <tarunduttaz@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	formation of lowering operator and raising operator
Date	2011-05-19 11:40 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<ir2vj9$gsd$1@smc.vnet.net> (permalink)

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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

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formation of lowering operator and raising operator tarun dutta <tarunduttaz@gmail.com> - 2011-05-19 11:40 +0000
  Re: formation of lowering operator and raising operator Peter Breitfeld <phbrf@t-online.de> - 2011-05-20 10:34 +0000
  Re: formation of lowering operator and raising operator Ray Koopman <koopman@sfu.ca> - 2011-05-21 10:47 +0000

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