/sci/ - Science & Math

>>10361484
a fancy way to write inner products. the key is to realize an inner product consists of two things: an operator and a vector

Usually we write something like (u dot v), bu tin QM you really need to write it as (u dot) (v), because the (u dot) is a vectorspace all unto it's own (called a dual space). With finite dimension spaces, this isn't important, but when you go to both countable and uncountable infinite dimensional vectorspaces, it's critical. For instance, the typical way to describe the free particle is as a linear combination of sinusoids, however these aren't normalizable, but linear combinations of them are (see Rigged Hilbert Space and Gelfand Triples)

dirac notation just writes shit as <u| and |v>, called a bra and a ket, respectively.