Re: Help on functions of noncommuting operators

On 19 Set, 02:32, tadchem <tadc...@xxxxxxxxxxx> wrote:
On Sep 18, 7:27 am, "sirjo...@xxxxxxxx" <sirjo...@xxxxxxxx> wrote:





On 16 Set, 22:25, tadchem <tadc...@xxxxxxxxxxx> wrote:

On Sep 16, 4:52 am, "sirjo...@xxxxxxxx" <sirjo...@xxxxxxxx> wrote:

Hello,
I study for hobby quantum physics, alone, and I am stuck with this
probably simple problem; A and B are operators and x is a parameter;
develop in series of powers of x the function

f(x)=1/(A+xB)   A and B do not commute

What do A and B operate upon?

How is xB defined?

Are A and xB compatible for addition.

Is the "reciprocal" of an operation (that is 1/A or 1/B) defined?

Is x a scalar or a vector or an operator?

If we derive df/dx do we get -B/(A+xB)^2  ?

That depends entirely upon the definitions of A, B, and x, of
differentiation within this particular manifold, and whether the
operations of 1/ and ^2 are defined.

Tom Davidson
Richmond, VA

Tom, the excercise does not say anything else than what I said; it
should be solvable as is.
Thanks
Sergio

Was this "exercise" on page one of the book?

If not, then there was a context for the problem.

Read the appropriate chapter to find out the context.

The context will add meaning to the notation.

Maybe you could even find a little more information to share with us.

Try posting the problem *verbatim* and telling us which chapter of
which book is its home.

Tom Davidson
Richmond, VA- Nascondi testo citato

- Mostra testo citato -

This is excercise 2.10 of the mathematical introductory chapter of the
Zettili:
Assuming that the inverse A^-1 of an operator A exists:
a) Evaluate (A-xB)^-1 in terms of the powers of x
b) If A and B commute show that the previous result is identical to
the classical expression, where A and B are treated as ordinary
parameters.

That's it, I believe this is supposed to be a simple exercise without
any complex assumptions!

Bye

Sergio
.

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