Do you know what this particular unitary operator is?

1. Jun 21, 2005

QMrocks

Recall that the unitary operator $exp(\frac{i}{\hbar}aX)$ transform the operator $P_x +a$ to $P_x$.

Now, what is the unitary operator that transform the operator $P_x +aX$ to $P_x$ ??

2. Jun 21, 2005

seratend

you mean P_x to P_x + a

$exp(- \frac{i}{\hbar}aX)$

: )

Seratend.

$exp( \frac{i}{\hbar}aX^2/2)$ is the answer to your question

Last edited: Jun 21, 2005
3. Jun 21, 2005

QMrocks

Nope...........................

4. Jun 21, 2005

QMrocks

There is no typo.

5. Jun 21, 2005

seratend

See corrected previous post.

Seratend.

6. Jun 21, 2005

QMrocks

Thanks. Thats the answer i tempted to throw in too. But i have my doubts..

7. Jun 21, 2005

seratend

Doubts, why? You just have to calculate.
Hint: try to see what the unitary operator exp(i a(X)) does on the momentum operator.

Seratend.

8. Jun 21, 2005

QMrocks

My bad, Seratend. You are absolutely right! Case close :)