Consider two operators A and B such that A, B = cI, where c is a complex number and I is the identity operator. Using the Baker-Cambell- Hausdorff identity: exp (A) exp (В) = exp (A + B+ A, B] + ([A, [A, B] + [B, [B, A]]) – . . .), determine which one of the following identity is correct?
Consider two operators A and B such that A, B = cI, where c is a complex number and I is the identity operator. Using the Baker-Cambell- Hausdorff identity: exp (A) exp (В) = exp (A + B+ A, B] + ([A, [A, B] + [B, [B, A]]) – . . .), determine which one of the following identity is correct?
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![Consider two operators A and B such that [A, B] = cI, where c is a complex number and I is the identity operator. Using the Baker-Cambell-
Hausdorff identity:
еxp (A) exp (B) — ехp (A + В + 3[A, B] + 3(4, [A, B] + [в, [В, А]) — .--) ,
determine which one of the following identity is correct?
А.
exp (A) exp (В) — еxp (A + В)
В.
exp (B) exp (А) — еxp (A + В)
C.
exp (B) exp (A) — еxp (A + В+ }{А, В)
D.
exp (A) еxp (B) — еxp (A + В + 3А, B)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4b63c57-0331-484a-876a-d4eb73967dee%2Fdc8f5d73-23d7-4186-a35d-7992b63c00a6%2F2lf8rv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider two operators A and B such that [A, B] = cI, where c is a complex number and I is the identity operator. Using the Baker-Cambell-
Hausdorff identity:
еxp (A) exp (B) — ехp (A + В + 3[A, B] + 3(4, [A, B] + [в, [В, А]) — .--) ,
determine which one of the following identity is correct?
А.
exp (A) exp (В) — еxp (A + В)
В.
exp (B) exp (А) — еxp (A + В)
C.
exp (B) exp (A) — еxp (A + В+ }{А, В)
D.
exp (A) еxp (B) — еxp (A + В + 3А, B)
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