When You're a Ket by Prof. Paul Halpern, University of the Sciences in Philadelphia Tune: "When You're a Jet " (aka "Jet Song"), from "West Side Story" by Leonard Bernstein) Midi file courtesy of hamienet.com (edited by WFS) Click here to stop music playback When you’re a ket You’re a ket all the way From a simple singlet To a Spin 2 array   When you’re a ket You’ve got brothers in place You belong to a set Of a complete Hilbert space   You’re never alone You’ve always got a bra state Proud columns you roam Not rows- that lie prostrate Even when you rotate   If you’re a ket In the basis of | p > Or the basis of | x > Doesn’t matter to me   If you’re a ket You are well normalized You’re as free as you get In a box, well or slice You’re never afraid Of projection operators If they single you out To try- and negate ya You can pop back later   Now here’s a vignette From- great Albert’s past Never believed in these rules Never thought they could last   But when you’re a ket You can change your own fate Just a roll of the dice You’re a new quantum state   If EPR’s true You’ve got instant communication A flip of your spin All your pals in syncopation Will do quick rotations   And then you are set With your own special Psi That you’ll never forget Til your probability’s nigh On a ket you can rely!

Paul Halpern is the author of many books about physics and astronomy aimed at general audiences, some of which are shown below. Click on any of the covers to find out more, or to purchase from amazon.com: . . .. The "bra-ket" notation was invented in 1930 by Paul Dirac. The "ket", for example |B>, represents the state of a quantum system. A "bra" is a "Hermitian adjoint" of a ket (e.g. <A| is the bra version of the ket |A>). The bra version basically means the same thing as the ket version, but is expressed mathematically in a way that allows us to take an inner product, e.g. <A|B>. This gives the probability amplitude for a particle in the state |B> to transition to the state |A>. The somewhat silly terminology of putting together a "bra", such as <A|, with a "ket", such as |B>, to form a "bra-ket" or "bracket", <A|B> is proof that physicists do have a sense of humor!   The tune for this song is from Leonard Bernstein's "West Side Story". Click here to purchase the soundtrack from amazon.com.