answer all 3 parts and show your working 2 a quantum system is modelled by the hamiltonian matri

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Question

2) A quantum system is modeled by the Hamiltonian matrix [ 0 h ] [ h 0 ] The orthonormal basis states are |1), |2), |3), such that the matrix elements are (1|H|1) = h, (2|H|3) = -h, etc. i) Find the eigenvalues of H. What are the possible outcomes when the energy is measured? [2] ii) Show that the normalized energy eigenstates |a), |b), |c) are |a) = |1) |b) = (|2) + |3) |c) = (|2) - |3) What are the energies that correspond to these eigenvectors? [1] iii) The system initially is prepared as the state |(t=0) = (2|1) + i|2) = âˆš5 Show that [1]

          2) A quantum system is modeled by the Hamiltonian matrix
[ 0   h ]
[ h   0 ]

The orthonormal basis states are |1), |2), |3), such that the matrix elements are (1|H|1) = h, (2|H|3) = -h, etc.

i) Find the eigenvalues of H. What are the possible outcomes when the energy is measured?
[2]

ii) Show that the normalized energy eigenstates |a), |b), |c) are
|a) = |1)
|b) = (|2) + |3)
|c) = (|2) - |3)

What are the energies that correspond to these eigenvectors?
[1]

iii) The system initially is prepared as the state |(t=0) = (2|1) + i|2) = âˆš5

Show that
[1]

answer all 3 parts and show your working 2 a quantum system is modelled by the hamiltonian matrix 0 hhw 0 the orthonormal basis states are 123 such that the matrix elements are 1h1 h 2h3 h e 97252

Added by Stephen M.

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