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