Solution
= Solution
In the ordered <basis> $(|0\rangle,|1\rangle)$,
$$
B=\begin{pmatrix}0&1\\0&0\end{pmatrix},\qquad
B^\dagger=\begin{pmatrix}0&0\\1&0\end{pmatrix},\qquad
H=\begin{pmatrix}0&0\\0&1\end{pmatrix}.
$$
= Solution
In the ordered <basis> $(|0\rangle,|1\rangle)$,
$$
B=\begin{pmatrix}0&1\\0&0\end{pmatrix},\qquad
B^\dagger=\begin{pmatrix}0&0\\1&0\end{pmatrix},\qquad
H=\begin{pmatrix}0&0\\0&1\end{pmatrix}.
$$