# Eigenvalues, eigenvectors, and time evolution.

A. Given matrix A = 1 2 0 where i found the eigenvalues to be 3hw, 0, -3hw.

2 0 2

0 2 -2

then if at t=0 state-vector is 1 THEN compute the state vector at time t.

0

0

Please explain me how to get this, Im very confused. I know its some sort of matrix multiplication but why?

b. If A = 1 0 0 is an observable. FIND its expectation at time t and compute the

0 2 0

0 0 0

probability that measuring A at time t gives the result 1.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/physics/quantum-physics/eigenvalues-eigenvectors-and-time-evolution-3eri