Recent content by physicslover123

So the issue is that ##P: \mathcal{H} \rightarrow V## is any projector from the whole space to a subspace ##V##. This subspace may not necessarily be ##S## in general. If that's the case, then a vector in ##S## can acquire a component orthogonal to ##S## under the projection. The way I'm reading...

Yes I have, and it is not idempotent in general because we don't necessarily know that P(|x>) \in S for |x>\in S, in other words the projector must be invariant on the subspace S, but that may not be true in general

I'm not entirely sure how to approach part 1. I tried the following: Call the span of the two states S. We can decompose H = S + S_perp. We consider some projector P: H -> V where V is some subspace of H. I made a new operator P_s P P_s where P_s is the orthogonal projector onto S. However, I...