Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: Commutators and Operator Powers in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg16739] Re: [mg16635] Commutators and Operator Powers in Mathematica
• From: "Nguyen N. Anh" <anh at chm.ulaval.ca>
• Date: Wed, 24 Mar 1999 02:23:52 -0500
• References: <199903191753.MAA09744@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

Hi Alan,

We've developed a code to deal with noncommutative commutator algebra. Althouch
it's been done with physics applications in mind, it can be easily extended to
handle other math expressions.

Please take a look at:

Computer Physics Communication, 115 (1998) 183-199

Best regards


On Mar 19, 12:53pm, Alan Lewis wrote:
> Subject: [mg16739] [mg16635] Commutators and Operator Powers in Mathematica
> I am looking for any links or suggestions on implementing
> commutation relations  and powers of differential operators
> in mathematica.
>
> As an example, I have two operators L0 and L1 that act on arbitrary
> (well say infinitely differentiable) functions f[x]
>
>  L0 simply multiplies f[x] by x.
>  L1  = a x^(3/2) D[f[x],x] + b x^2 D[f[x],{x,2}]
>
> where a,b are constants independent of x. The second line is not
> meant to be working math. code but is just meant to explain the action
> of this differential operator.
>
> Now what I want to do is be able to evaluate repeated commutators
> and powers of these operators. For example, the first commutator
> should evaluate to:
>
> [L0,L1]f[x] = x L1 f[x] - L1 (x f[x]) =
>
>              -a x^(3/2) f[x] - 2 b x^2 D[f[x],x]
>
> I would also like to evaluate powers such as
> L1^n, meaning the operator acts on f[x] n times. Repeated
> commutators are expressions like
>
> [L1,[L0,L1]] or [L0,[L0,L1]], etc.
>
> The action of L1 is just an example, but the general class of operators
> I am interested in are always the sum of a first and second derivative
> with simple expressions like the above in front of the derivative.
> And L0 is always multiplication by x.
>
> Thanks in advance for any suggestions,
> Alan
>-- End of excerpt from Alan Lewis



-- 
Nguyen Nam Anh   Quebec, Canada
E-mail: anh at chm.ulaval.ca
WWW: http://promethium.chm.ulaval.ca/~anh/

• References:
  • Commutators and Operator Powers in Mathematica
    • From: Alan Lewis <alanlewis@home.com>