#translation operator

Commutators for some symmetry operators

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Q: [1] pr 4.2

If \( \mathcal{T}_\Bd \), \( \mathcal{D}(\ncap, \phi) \), and \( \pi \) denote the translation, rotation, and parity operators respectively. Which of the following commute and why

(a) \( \mathcal{T}_\Bd \) and \( \mathcal{T}_{\Bd’} \), translations in different directions.

(b) \( \mathcal{D}(\ncap, \phi) \) and \(…

SHO translation operator expectation

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Question: SHO translation operator expectation ([1] pr. 2.12)

Using the Heisenberg picture evaluate the expectation of the position operator \( \expectation{x} \) with respect to the initial time state

\begin{equation}\label{eqn:translationExpectation:20} \ket{\alpha, 0} = e^{-i p_0 a/\Hbar} \ket{0}, \end{equation}

where \( p_0 \) is the…