Physics 410 Midterm Practice Exam Fall 2007, Frey Closed book ...

5. (15 points)
( )
( )
1 0
Two basis vectors, |v 1 〉 = and |v
0
2 〉 = are transformed by a matrix
1
( )
0 1
S =
to a rotated basis S |v
−1 1
1 〉 = |v 1〉 ′ and S |v 2 〉 = |v 2〉 ′ .
(a) Determine |v ′ 1〉 and |v ′ 2〉 .
(b) If an operator A is represented in the original basis by the matrix A =
what is its representation A ′ in the rotated basis?
(
−1 2
2 0
)