4. Calculate the following commutators(Recall that [Â, B] = ÂB – BÂ= -[B, Â)(a) [â, î](b) [â, î](c) [â²,p](d) [â, ƒ(â)](e) [p, f(â)](f) [î, H] for general potential V (x)

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4. Calculate the following commutators (Recall that [Â, B] = ÂB – BÂ= -[B, Â]) (a) [&, 최 (b) [â, p] (c) [â², p]

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Question

Expert Solution

Step 1

Given,

commutator is,

$[\hat{x}, \hat{x}]$

solving this,

$\begin{array}{rcl} [\hat{x}, \hat{x}] & = & (\hat{x} \hat{x} - \hat{x} \hat{x}) \end{array}$

Since position operator is written as $\hat{x} = x$

Then

$\begin{array}{rcl} [\hat{x}, \hat{x}] & = & (x x - x x) \\ = & 0 \end{array}$

so commutation relation of $[\begin{array}{rcl} \hat{x} \end{array}, \begin{array}{rcl} \hat{x} \end{array}]$ is 0

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