Re: " f^ [n](x) = exp( n/ phi' (x) D ) o x "


"G. A. Edgar" <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:040520061551393458%edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
In article <1146765273.121843.263350@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<"alainverghote@xxxxxxxx"> wrote:

Dear Edgar ,

an other writing seems to be :
sum( k from 0 to infinity 1/ k! * { n / phi '(x) * d/dx } ^ k ) o
x .

What is that x on the end. A function? A variable?
If it is a variable, how do you compose with it?
Should the ending be " ... ^k)(x) " and not " ... ^k) o x " ??


I think he meants that the operator is acting x.

For example, one has the evolution operator psi(t) = e^(aHt)*psi(0)

which tells how psi evolves in time

or equivilently

sum((aHt)^k/k!,k=0..infinity)*psi(0)

(aHt)^k = a^k*t^k*H^k

so

sum((at)^k/k!*H^k*psi(0),k=0..infinity)

and H acts on psi(0)


if H^k = d^k/dx^k for k>0 and H^0 = 1 then the sum above is psi(0).

So potentially he could be talking about some quantum mechanical system but
I don't know since I don't know what phi and n represent.. the o is another
mystery.


.