IGNOU MPH 8 2026 - Write the space translation operator in quantum mechanics f

Question

Write the space translation operator in quantum mechanics $\hat{T}(a)$ for a finite translation a along the x direction. Calculate the commutator $[\hat{x}, \hat{T}(a)]$ . You may use the Baker-Campbell-Hausdorff formula: $e^{\hat{A}} \hat{B} e^{-\hat{A}} = \hat{B} + [\hat{A}, \hat{B}] + \frac{1}{2} [\hat{A}, [\hat{A}, \hat{B}]] + \dots$

19 Jan 2026

Answer :

Word Count : 172

The space translation operator for a finite translation (a) along the (x)-direction in quantum mechanics is defined as: [ \hat{T}(a) = e^{- \frac{i}{\hbar} a \hat{p}_x} ] where (\hat{p}_x) is the momentum operator along (x). To calculate the commutator ([\hat{x}, \hat{T}(a)]), we use the Baker-Campbell-Hausdorff (BCH) formula: [ e^{\hat{A}} \hat{B} e^{-\hat{A}} = \hat{B} + [\hat{A}, \hat{B}] + \frac{1}{2!}[\hat{A},[\hat{A},\hat{B}]] + \dots ] Let (\hat{A} = -\frac{i}{\hbar} a \hat{p}_x) and

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