Problems for Edward F. Redish |
A two mass system where each mass can be displaced in one dimension is described as a linear space spanned by the basis vectors
.
Suppose the normal modes of the system are found to be described by the orthonormal set of vectors
where α, β, γ, and δ could be complex.
(a) If we choose to describe these 4 vectors as Dirac states, |f_{i}>, i = 1,2 and |e_{i}>, i = 1,2, find the 8 inner products <e_{i}|f_{i}> and <f_{i}|e_{i}>.
(b) What is the matrix (in the f-basis) that represents the sum ?
(c) A vector is represented in the f-basis by the sum . This same vector is represented in the e-bases by . Find the A'_{i} in terms of the A_{j}.
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Last revision 7. December, 2005.