Re: commutators and translation operators


boris@xxxxxxxxxxxxxxxxxx wrote:
> Hi,
>
> I'm currently working through Julian Schwinger's "Quantum Mechanics"
> book and there's an exercise I cannot solve. Below q and p are
> operators with [q,p] = i and q' is a number.
>
> -----
> Ex. 1-55: Arrange
>
> [1]: exp(-i f(q)) exp(i q' p) exp(i f(q))
>
> in different ways

Hi, Boris.

I noticed that nobody has posted to your thread since the twenty-second
so I thought I'd have a go at it.

How many and in which different ways can you arrange the terms?

If I read them right, I see

e^(-i * f(q)) * e^(i * q' * p) * e^(i * f(q))

so would

e^( (-i * f(q)) + (i * f(q)) + (i * q' * p))

lead to the simplification

e^(i * f(q))?

Poor lonely thread....

Doug Goncz
Replikon Research
Seven Corners, VA 22044-0394

.