Q92 · CSIR NET Chemistry, June 2014
Paper: CSIR NET June 2014 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Medium
Two different non-zero operators $\hat{A}$ and $\hat{B}$ $(\hat{A}\neq\hat{B})$ satisfy the relation $(\hat{A}+\hat{B})(\hat{A}-\hat{B})=\hat{A}^{2}-\hat{B}^{2}$
(a)$\hat{A}\hat{B}=\hat{A}^{2}$ and $\hat{B}\hat{A}=\hat{B}^{2}$
(b)$\hat{A}\hat{B}+\hat{B}\hat{A}=0$
(c)$\hat{A}$ and $\hat{B}$ are arbitrary
(d)$\hat{A}\hat{B}-\hat{B}\hat{A}=0$
Answer
Answer: D ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
(A+B)(A−B) = A² − AB + BA − B². This equals A² − B² only if AB − BA = 0 (d).
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