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>
- Commutators and Operator Powers in Mathematica