Do you know what this particular unitary operator is?

QMrocks

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

Now, what is the unitary operator that transform the operator [itex] P_x +aX [/itex] to [itex] P_x [/itex] ??

seratend

you mean P_x to P_x + a

[itex] exp(- \frac{i}{\hbar}aX) [/itex]

: )

Seratend.

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

QMrocks

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

QMrocks

There is no typo.

seratend

See corrected previous post.

Seratend.

QMrocks

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

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.

QMrocks

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