- #1
abcs22
- 11
- 0
Homework Statement
Vectors I1> and I2> create the orthonormal basis. Operator O is:
O=a(I1><1I-I2><2I+iI1><2I-iI2><1I), where a is a real number.
Find the matrix representation of the operator in the basis I1>,I2>. Find eigenvalues and eigenvectors of the operator. Check if the eigenvectors are orthonormal. [/B]
Homework Equations
Av=λv
The Attempt at a Solution
My problem is concerning the first part of this excercise. I'm not really familiar with this notation of the operator and not sure how I should get the matrix. I have tried improvisation and got the matrix
2a^2 -2a^2
-2a^2 2a^2
When I tried to calculate eigenvalues, I didn't get anything reasonable, so I believe that my matrix is wrong. Please help me regarding this problem, once I have the right matrix I will not have the problem finding eigenvalues nor eigenvectors.