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 $\hat{\mathrm{A}}$ and $\hat{\mathrm{B}}(\hat{\mathrm{A}} \neq \hat{\mathrm{B}})$ satisfy the relation $(\hat{\mathrm{A}}+\hat{\mathrm{B}})(\hat{\mathrm{A}}-\hat{\mathrm{B}})=\hat{\mathrm{A}}^{2}-\hat{\mathrm{B}}^{2}$
(a)$\hat{\mathrm{A}} \hat{\mathrm{B}}=\hat{\mathrm{A}}^{2}$ and $\hat{\mathrm{B}} \hat{\mathrm{A}}=\hat{\mathrm{B}}^{2}$
(b)$\hat{\mathrm{A}} \hat{\mathrm{B}}+\hat{\mathrm{B}} \hat{\mathrm{A}}=0$
(c)$\hat{\mathrm{A}}$ and $\hat{\mathrm{B}}$ are arbitrary
(d)$\hat{\mathrm{A}} \hat{\mathrm{B}}-\hat{\mathrm{B}} \hat{\mathrm{A}}=0$
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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