This question is from the text book 'Quantum Mechanics' second edition by David J. Griffiths.
(See attached file for full problem description)
Problem 3.5 - The hermitan conjugate (or adjoint) of an operator Qprime...
Problem 3.7 - The Hamiltonian and the initial state for a certain three-level system is given. Find its state at a time t
Hermitian conjugate of different operators are derived. The method to determine the state of a three level system at a time 't' is explained given its initial state (at time t=0) and the Hamiltonian matrix.