Do you know what this particular unitary operator is?

by QMrocks
Tags: operator, unitary
 P: 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 $P_x$ ??
P: 318
 Quote by 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 $P_x$ ??
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
P: 85
 Quote by seratend $exp(- \frac{i}{\hbar}aX)$ : ) Seratend.
Nope...........................

P: 85

Do you know what this particular unitary operator is?

There is no typo.
P: 318
 Quote by QMrocks There is no typo.
See corrected previous post.

Seratend.
P: 85
 Quote by seratend 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..
P: 318
 Quote by QMrocks 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.
 P: 85 My bad, Seratend. You are absolutely right! Case close :)

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