Answer to Question #282973 in Quantum Mechanics for BIGIRIMANA Elie

Question #282973

 If A, B and C are Hermitian operators, determine if the following combinations are Hermitian: (a) A + B (b) 1 2i [A, B] (c) (ABC − CBA) (d) A2 + B2 + C 2 (e) (A + iB)


1
Expert's answer
2022-02-09T09:15:10-0500

Answer

Given that


A, B ,C are Hermitian operators

So

"\\hat{A}^+=\\hat{A}\\\\\\hat{B}^+=\\hat{B}\\\\ \\hat{C}^+=\\hat{C}"

Therefore checking hermitian

"(a) (A + B ) ^+= A^+ + B^+\\\\= A + B"

"(b) (2i[A , B ] )^+=(-2i) [B,A]\\\\=2i [A , B ]"

d) "(A^2 + B^2+C^2 ) ^+\\\\= A^2 + B ^2+C^2"

So options a b d are Hermitian and other are not.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS