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for example, if I had [tex] H = H_0 + W = \left(\begin{array}{cc}a&c\\b&d\end{array}\right) = \left(\begin{array}{cc}a&0\\0&d\end{array}\right) + \left(\begin{array}{cc}0&c\\b&0\end{array}\right)[/tex]

Is it true to say that H

_{0}is still in the basis [tex]{|x\rangle, |y\rangle} [/tex], and if it is, is there a way I could determine what [tex]|x\rangle[/tex] and [tex]|y\rangle[/tex] actually look like?