Do you know what this particular unitary operator is?

1. QMrocks

85
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. seratend

318
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. QMrocks

85
Nope...........................

4. QMrocks

85
There is no typo.

5. seratend

318
See corrected previous post.

Seratend.

6. QMrocks

85
Thanks. Thats the answer i tempted to throw in too. But i have my doubts..

7. seratend

318
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. QMrocks

85
My bad, Seratend. You are absolutely right! Case close :)