to avoid confusion i put the symbol on top of operators 1 the hamilton
To avoid confusion, I put the symbol "" on top of operators.
1.The Hamiltonian of a two-state system is:
Ap = (2 721 ²-21)
a) (1 point) Verify that He is Hermitian.
b) (3 points) Find eigenvalues of Fo
c) (3 points) Find eigenvectors of Ho
d) (3 points) Consider the state ) = (
What are the possible outcomes of the experiment in which the energy of the particle in state
1o) is measured? What are the probabilities of the possible outcomes?
Hint: It would be easier if you normalize (o) and the two eigenvectors first.
e) (2 points) Solve the time-dependent Schrödinger equation:
with the initial condition: (t = 0)) = 1o) = (3), i.e., derive expressions for the components
a(1) and b() of the solution 14(t)) = (())
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