Problems for
Intermediate Methods in Theoretical Physics

Edward F. Redish

Changing Bases in Dirac Notation

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, |fi>, i = 1,2 and |ei>, i = 1,2, find the 8 inner products <ei|fi> and <fi|ei>.

(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 Aj.


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Edward F. Redish
Department of Physics
University of Maryland
College Park, MD 20742
Phone: (301) 405-6120

Last revision 7. December, 2005.