Edward F. Redish
In a 2-D Cartesian vector space the basis is expressed in Dirac notation as
An arbitrary vector is expressed in this basis as
Suppose we consider a new basis rotated from the first by an angle θ as shown in the figure at the right:.
(a) Construct the 8 dot products
(b) Use the dot products you have constructed to express the coordinates of the vector |A> in the new basis, a1', a2', in terms of the old coordinates, a1, a2.
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Last revision 28. November, 2005.