Problems for Intermediate Methods in Theoretical Physics 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.

RETURNS

University of Maryland	Physics Department	Physics 374 Home

Last revision 7. December, 2005.