Just a few notes here about shiny things that caught my eye regarding bra and ket notation in the quantum mechanics II lecture last night. Inner Products Inner products are the Hilbert space, quantum mechanical, state vector equivalent of the dot product for more standard vectors like position or velocity. The unit basis ket , at least in our class, is written as where j is the index of the component. Associating back to Cartesian coordiantes, 1 would denote x, 2 would denote y, and 3 would denote z. The ket vector is the same symbol in a ket and when the two are applied to each other we get the inner product . In other words, the inner product only produces contributions from like basis vectors, just like the dot product. So here's the cool bit, the following all accomplish about the same thing, they find a number proportional to the magnitude of the component of one vector, lying along another vector whether those vectors are what we most ty...