Do you know what this particular unitary operator is?

[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 $P_x$ ??

 

[seratend]

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 $P_x$ ??

you mean P_x to P_x + a

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

: )

Seratend.

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

 

[QMrocks]

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

: )

Seratend.

Nope......

 

[QMrocks]

There is no typo.

 

[seratend]

There is no typo.

See corrected previous post.

Seratend.

 

[QMrocks]

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

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

 

[seratend]

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

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.

 

[QMrocks]

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