Subspaces in Hilbert Space

In Chapter 3 we used two-dimensional Hilbert space to model a manual for measuring electron spin, because every experiment had only two outcomes: spin-up and spin-down. Of course, many physical experiments have outcome sets that are not finite. A measurement of energy, position, or momentum of a moving particle usually means obtaining an outcome from an infinite number of possibilities. In this chapter we shall learn about infinite dimensional Hilbert spaces. In particular, we shall consider the subspace structure of infinite dimensional Hilbert spaces. These provide the logics for orthodox quantum physics.