The following kets name vectors in the Euclidean plane:
|a>, |b>, |c>.
Some inner products: = 1, = −1, = 0, = 1, = 1
(a) Which of the kets are normalized?
(b) Which of these are an orthonormal basis?
(c) Write the other ket as a superposition of the two basiskets. What is the norm |h·|·i| of this ket (i.e., the length of thevector)? What is the angle between this ket and the two basiskets?
(d) In the same basis, write as a superposition a ket that hasthe same direction but is normalized.
