- #1

tanaygupta2000

- 208

- 14

- Homework Statement
- Consider an N-dimensional linear vector space spanned by the ortho-normal basis

states, {|b1>, |b2>, ...., |bN>}. An operator R is given to operate on these basis stats as: R|b(j) = |b(j+1)> for j=1 to (N-1), and R|bN> = |b1>.

Write R in the matrix form in the given basis.

- Relevant Equations
- <ψ|R|ψ> = Σ(i) Σ(j) <ψ|bj> <bj|R|bi> <bi|ψ>

where

R operator = <bj|R|bi> matrix

I have successfully found the N by N matrix corresponding to the operator R.

But the problem is, whenever I try to operate R on |bj> basis vectors, I am not getting |b(j+1)> as it should be.

Instead, I am getting result as given in the question only by <bj|R = <b(j+1)|

Matrix is not working with kets.

Please help !